Regeneration energy, also known as regenerative energy or Time Lord energy, (PROSE: The Christmas Inversion) was the energy a Time Lord produced as a product of regenerating. A Time Lord typically had enough natural energy to regenerate twelve times which gave them their thirteen lives, (TV: The Deadly Assassin) although the High Council could provide an individual with another cycle of energy should they desire, (TV: The Five Doctors) as in the case with the Master, (TV: The Sound of Drums, AUDIO: Day of the Master) and the Doctor. (TV: The Time of the Doctor)
Even after expending their allotted twelve regenerations, a Time Lord still possessed some regeneration energy in their final life, as demonstrated by the Eleventh Doctor. (TV: The Angels Take Manhattan, The Time of the Doctor) Azmael showed that a Time Lord could initiate a thirteenth regeneration that would result in their death. (TV: The Twin Dilemma) If a Time Lord died with no full regenerations left, their body could release one last burst of regeneration energy which caused the corpse to vanish altogether, although one had to will this to happen prior to death (PROSE: Shada) and this was never seen to happen to a Time Lord who died because they were killed in a way preventing regeneration, rather than at a point where they had expended all their lives. (TV: The Doctor Falls)
Regeneration energy was typically golden in appearance, (TV: The Caves of Androzani, The Parting of the Ways, The End of Time, Day of the Moon, Let's Kill Hitler, The Night of the Doctor, The Day of the Doctor, The Time of the Doctor, Hell Bent, The Doctor Falls, Twice Upon a Time, The Timeless Children) but it could occasionally be a bright ray of colours instead. (TV: Time and the Rani, Utopia) It could also take the form of electricity. (TV: Doctor Who) In one instance, the energy was visible through the Thirteenth Doctor's skin, on her arms and veins, exhibiting she had two pulses. (TV: The Woman Who Fell to Earth)
It occasionally trickled from the hand as a sign of imminent regeneration, varying from barely noticeable, (TV: The Parting of the Ways, The Stolen Earth, The End of Time, The Doctor Falls, Twice Upon a Time) to clearly visible. (TV: Day of the Moon, Let's Kill Hitler, The Night of the Doctor, The Time of the Doctor, The Doctor Falls, Twice Upon a Time) It also flowed from other body parts, typically the face, head and neck (TV: The Parting of the Ways, Utopia, The End of Time, The Time of the Doctor, Twice Upon a Time, The Woman Who Fell to Earth, AUDIO: The Brink of Death) or sometimes feet. (TV: The Timeless Children) Although, at least in the Doctor's case, some regenerations did not yield any noticeable display of regeneration energy, merely transitioning from one body to the next (TV: Planet of the Spiders) or to a cocooned state inbetween. (TV: Logopolis)
Iris Wildthyme's entire body glowed a bit when she regenerated into her Jane Fonda incarnation. (PROSE: The Scarlet Empress) The Hermit also emitted a blazing light when he regenerated. (PROSE: The Taking of Planet 5)
Regeneration energy, as it engulfed the regenerating individual, would sometimes emit a high-pitched trill not unlike the sound of a sonic screwdriver. (TV: The Parting of the Ways, Twice Upon a Time et al.)
The energy itself was quite powerful, typically encouraging those nearby to back away, (TV: The Parting of the Ways, The Stolen Earth, Let's Kill Hitler) and caused significant damage to the Doctor's TARDIS more than once. (TV: The End of Time, Twice Upon a Time) It could also be used as a weapon; River used it to knock down several soldiers after they shot her, (TV: Let's Kill Hitler) and the Eleventh Doctor was able to destroy an entire Dalek fleet when he started regenerating. (TV: The Time of the Doctor) The Tenth Doctor could also use the regeneration energy stored up in a circuit of the TARDIS to disintegrate a platoon of Cybermen. (TV: The Age of Steel) The Eleventh Doctor also claimed that his regeneration energy could destroy the Cyber-Planner Mr Clever, (TV: Nightmare in Silver) and transmitting it on a large scale allowed Rassilon and the Twelfth Doctor to burn off cyber-implants across the totality of the Cyberiad. (COMIC: Supremacy of the Cybermen) The energy stored up in Donna Noble's mind was powerful enough to blast several copies of the Saxon Master down when triggered by her remembering the Doctor's face, though it knocked her out for several hours as well. (TV: The End of Time)
The energy also sometimes brought the Time Lord regenerating extreme pain; the Ninth Doctor stumbled back as some surged from his hand, and he continued clutching his torso in pain until he submitted to the process. (TV: The Parting of the Ways) The War Master and Mels screamed in agony while purging themselves of the energy, (TV: Utopia, Let's Kill Hitler) and the Eighth Doctor collapsed to the floor, groaning, when his regeneration started. (TV: The Night of the Doctor) The Tenth Doctor briefly collapsed and struggled to walk towards his TARDIS because of the pain. The Eleventh Doctor initially cried out in pain when emerging from the Tenth Doctor's explosive regeneration. (TV: The End of Time) The Twelfth Doctor continuously stumbled and fell while resisting his own regeneration, making pained noises during the process. (TV: Twice Upon a Time)
The Tenth Doctor remarked that the energy was in excess for roughly 15 hours after regenerating, enabling him to restore his hand after it was chopped off. (TV: The Christmas Invasion) River Song was also able to survive being shot by a group of Nazi soldiers due to the excess energy. (TV: Let's Kill Hitler) The Thirteenth Doctor even survived a fall from a great height and crashing through a train's roof, surviving with no noticeable injuries or concussion. (TV: The Woman Who Fell to Earth, PROSE: Things She Thought While Falling) It was sometimes harmlessly expelled through the mouth, for a while after regeneration. (TV: The Christmas Invasion, The Eleventh Hour, The Woman Who Fell to Earth) The Twelfth Doctor also remarked that the energy created in the initial beginnings of regeneration could reignite a Time Lord's own life force, placing them in a "state of grace". Although, resisting the process would eventually backfire on them, leading to a severe loss of energy, requiring them to purge themselves of the energy and completely regenerate or continue to resist, leading to death. (TV: Twice Upon a Time)
The energy was capable of creating an entirely new individual based on the Time Lord who produced it. In one instance, the Tenth Doctor used up his eleventh regeneration while still keeping the same face by channelling it into his former hand, (TV: Journey's End) which was sliced off by Sycorax leader, (TV: The Christmas Invasion) allowing himself to heal his body, yet avoid physical changes. This regeneration energy remained active and was accidentally interacted with by a human, Donna Noble, triggering a two-way human-Time Lord meta-crisis which caused the hand to regenerate the missing body of its owner, creating a human-Time Lord copy of the Doctor and causing Donna to gain the mind of a Time Lord. However, the presence of two minds inhabiting Donna at once nearly destroyed her and the Doctor was forced to block all memories of him from her consciousness to stop her Time Lord half from remaining active. The Meta-Crisis Doctor also lacked the ability to regenerate. (TV: Journey's End)
The energy could also be conjured for use without the need to regenerate, though doing so was considered inadvisable because it could have repercussions on future regenerations. The Tenth Doctor transferred ten years of his life worth of the energy into a single living circuit in his TARDIS after it lost power when travelling into a parallel universe, giving it enough power that it could revive the entire dead TARDIS within 24 hours, although it would only be able to operate for five minutes in the parallel universe before it 'died' again unless returned to its own reality. (TV: Rise of the Cybermen / The Age of Steel) When River Song - in her third incarnation - used all of her remaining regeneration energy to bring the Eleventh Doctor back to life after she infected him with a fatal poison, the process nearly killed her and destroyed her ability to regenerate. (TV: Let's Kill Hitler) Even after he had used up all twelve of his regenerations, (TV: The Time of the Doctor) the Eleventh Doctor was able to conjure up enough regeneration energy to heal River's broken wrist. (TV: The Angels Take Manhattan) The Twelfth Doctor willingly expended some regeneration energy to restore Davros' eyesight while claiming it would also cost an arm or a leg down the line. (TV: The Witch's Familiar) His Shadow World counterpart used a device to siphon energy from his personal future to temporarily restore his own eyesight, speculating that there may be the potential cost of making all his future regenerations blind, not being able to regenerate again, or dying shortly after. (TV: Extremis) He also used regeneration energy when tricking Bill Potts into thinking he was helping the Monks, (TV: The Lie of the Land) and conjured a small portion of the energy to prove to his first incarnation that they were the same person. (TV: Twice Upon a Time)
Other uses & functions
As a food source
The alien race known as the Ravenous evolved to feed on regeneration energy, due to its similarity to the Kolstani's native food source, artron energy. (AUDIO: Day of the Master) This made them the predator of the Time Lords. Although they could also feed on humans, the Doctor compared this to humans settling for a packet of crisps before moving on to the main "steak dinner" of a Time Lord. (AUDIO: Seizure, Deeptime Frontier) However, Time Lords suffering from regenerative dissonance were essentially immune to the Ravenous, as their condition "contaminated" the regenerative energy, making it unappealing to the Ravenous. (AUDIO: The Odds Against) When the Master was occupying the body of a human, this 'tainted' his remaining regeneration energy to make it somehow unpalatable, although the Ravenous were willing to feed on the Master when he was returned to his natural body despite him lacking any regeneration energy at that point in his life. (AUDIO: Planet of Dust)
When the Eleven used the Crucible of Souls to grant all contemporary lifeforms in the universe the ability to regenerate, without end and without a need for change in physiognomy, he gave the Ravenous an endless supply of regeneration energy, on which to feed and multiply. (AUDIO: Day of the Master)
The essence of a Time Lord
When a Time Lord used a Chameleon Arch to turn themselves into another species while sealing away their memories and their Time Lord sense of self in a biodata module, the essence of the Time Lord within the module would take the form of the golden regeneration energy. It would be observed to stream back into the Chameleon Arch user when the biodata module was eventually opened, through the eyes (TV: Utopia) or the entire face. (TV: Fugitive of the Judoon)
As such, this form of regeneration energy was similar to the energy of the heart of the TARDIS; also appearing on many occasions as a golden shimmer, sometimes even with the telltale high-pitched trill, (TV: Doctor Who, The Parting of the Ways, The Doctor's Wife) this soul of the timeship could enter an organic body via its eyes, (TV: The Parting of the Ways) and was, for that matter, once seen to be able to resurrect two deceased humans, the Master's rebellious companion Chang Lee and the Eighth Doctor's paramour Grace Holloway. (TV: Doctor Who)
Behind the scenes
Evidence points towards the golden energy regeneration effect iconic to the BBC Wales revival of Doctor Who having come to be as a sort of serendipitous image: the golden energy look was first featured in 1996's TV Movie, where it was the form taken by a stream of energy from the TARDIS's heart and soul, the Eye of Harmony, which flew up from the closing Eye to bring Lee and Grace back to life. In Series 1 in 2005, the blinding golden glow was used in Boom Town to signify the unknowable Heart of the TARDIS, together with the first appearance of the familiar "high-pitched trill" sound effect; in another episode of the same season, Dalek, the same look was used (briefly) for the temporal power of the artron energy.
This effect then naturally appeared again when, in the season finale, Rose Tyler broke open the TARDIS control console to communicate with the TARDIS and absorb the energy of the Heart, an event conflated in dialogue with Rose having "absorbed the Time Vortex". As the power was beginning to kill Rose, the Ninth Doctor was then seen taking all this power from her and painfully containing it within himself, which was the cause of his regeneration into the Tenth Doctor. Consequently, as he regenerated, golden energy streamed from him, which viewers at the time understandably interpreted as the Doctor "letting go" and releasing the TARDIS's energy at the same time as he regenerated.
However, this was also the first time regeneration was seen in the revived Doctor Who, and consequently, when the time came to show the War Master regenerating into John Simm's incarnation of the Master as a way to establish beyond a shadow of a doubt that this newly-reintroduced character was in fact a Time Lord on par with the Doctor, it was decided to use a similar "streaming glow" effect to what had been done in The Parting of the Ways. As it became the iconic look of regeneration in the new series, subsequent on-screen regenerations (the Doctor's and otherwise) would then utilise variations of this effect, despite it quite possibly never having been intended to be a "regeneration energy" effect.
This new convention did not stop the glow effect from returning to its original purpose of depicting the TARDIS's power in Series 6's The Doctor's Wife; all this without a potential link between the artron energy at the heart of the TARDIS, and the regeneration energy of Time Lords, ever being addressed in-story, though the comic story Doorway to Hell interestingly recontextualised the Doctor's TARDIS repairing itself with a new desktop theme in The Eleventh Hour as TARDISses being capable of regeneration in their own right.
Adding to the complexity of all this was the 2017 Christmas Special Twice Upon a Time, a story which featured the Twelfth Doctor meeting the First Doctor, both on the brink of regeneration; the story showed the First Doctor displaying the familiar golden glow upon regeneration, retconning the blinding white light in 1966's black-and-white story The Tenth Planet, to have "actually" been golden as well. The Timeless Children, a 2020 episode which delved into the origins of regeneration on Gallifrey, even went so far as to suggest that the "first regeneration of any person on the planet of Gallifrey", the Timeless Child's first regeneration in front of the First Tecteun, used the orange-golden glow.
In Doctor Who and the Time War, Russell T Davies showed the Eighth Doctor as being briefly surprised that the energy that engulfs him was now golden, right before he figures out that he has been granted a new lease of life by the Restoration. This suggests that the Restoration is the reason post-Time-War regenerations are visually different from classic ones.