Jenny was the "daughter" of the Tenth Doctor, artificially created from his DNA when it was forcibly sampled by similarly cloned human warriors with a progenation machine.
During a short war on the planet Messaline between humans and Hath, both sides used progenation machines to instantly create mentally programmed adults from the DNA of single parents. When the Tenth Doctor, Donna Noble, and Martha Jones arrived on Messaline, Jenny was made from a skin sample taken from the Doctor, against his will. (TV: The Doctor's Daughter)
With the Doctor
The then nameless Jenny pushed a button which triggered an explosion. The tunnel collapsed, cutting the group off from the Hath and Martha. Shortly after, Jenny was named by the Doctor's companion Donna Noble from his description of her as a "generated anomaly".
Jenny's commander, Cobb, had the Doctor, Donna, and Jenny locked up. Donna proved to the Doctor that Jenny was indeed his daughter by listening to Jenny's heartbeat. Like the Doctor, she had two hearts. However, the Doctor insisted that she was nothing more than an "echo", and that a "real" Time Lord was "so much more".
As the three of them made their way towards the Source, which Cobb and the Hath both sought, Jenny spoke with the Doctor about the possibility of travelling with him, and he told her that he would never leave her. The Doctor told the respective parties to end the war, whereupon General Cobb aimed his gun and shot at him. Jenny jumped in the way of the bullet. She was shot through one of her hearts, and died, but did not regenerate. (TV: The Doctor's Daughter)
While lying in state, Jenny's body was revived by the gaseous compound from the Source. (REF: The Time Traveller's Almanac) With her father having left the planet and believing her to be dead, she stole a shuttlecraft and left Messaline. When asked where she was going, she restated Donna's earlier description of the Doctor's life. "Oh, I've got the whole universe: planets to save, civilisations to rescue, creatures to defeat – and an awful lot of running to do." She then set off to explore the universe. (TV: The Doctor's Daughter)
It is unknown whether Jenny had any contact with her father. But as he thought she was "dead", it seems unlikely that they would ever cross paths again.
Davros tried to manipulate the Doctor when he moved the Earth to the Medusa Cascade by asking the Doctor how many people had died in his name. Jenny was one of the people the Doctor thought of, as he was unaware of her revival. (TV: Journey's End)
Jenny showed a lot of the brilliance, lust for life, and determination of her father. She was also flirtatious. Though programming had made her military-minded and goal-oriented, she had too much of her father in her blood. While at first she showed violent intentions towards others, she soon adopted the Doctor's values and principles, though she also challenged him. (TV: The Doctor's Daughter)
She was delighted at the prospects of travelling in the TARDIS with her father and Donna. But after her revival, she did not seem bothered about the prospect of never seeing her father again, and was more excited about travelling the universe by herself.
Being biologically Gallifreyan, Jenny had two hearts, as well as reflexes, precision timing, and acrobatic ability far beyond that of an average human. (TV: The Doctor's Daughter) One report suggests that Jenny's revival was not due to regeneration, but instead the hidden properties of the Source. (REF: The Time Traveller's Almanac) At first the Doctor flatly denied that she should be considered a Time Lord, because she lacked the shared culture, code, and knowledge. While there is some evidence of a change in his opinion, ultimately he did not re-address the subject. (TV: The Doctor's Daughter)
The presence of Jenny drew the Doctor's TARDIS to Messaline, paradoxically before her creation, so that she, in effect, caused herself to exist. (TV: The Doctor's Daughter) River Song similarly caused herself to exist by encouraging her own parents to pursue their feelings for each other. (TV: Let's Kill Hitler)
Behind the scenes
Although not considered a companion of the Doctor's, Jenny can be, at least, considered a "companion presumptive". It is clear, once the Doctor accepted her as his daughter, that she would travel with him and Donna. Her "death" ended these plans. This places Jenny in the same category as Astrid Peth, Lynda Moss, Madame de Pompadour, and Rita, who were all invited to travel with the Doctor and accepted the invitation, yet died before they were able to do so; or Amelia Pond for the first twelve years after the Doctor invited her. Amelia's father-in-law (the Doctor's grandfather-in-law), Brian Williams, initially declined the Doctor's invitation to travel after having accidentally travelled with him on one occasion previously, but later accepted a trip to Siluria, and spent four days in the stationary TARDIS.
Steven Moffat is credited with suggesting that Jenny be brought back to life at the end of the episode. This led to rumours that Georgia Moffett was in the running to return as a companion for the Eleventh Doctor. Ultimately, Karen Gillan was cast in this role as Amy Pond.
Although The Sun, a UK tabloid newspaper, speculated that Georgia Moffet would appear as Jenny in one of the 2009 specials, she did not make an appearance. No further appearances of the character have been announced. Moffett did return to the franchise in other roles, providing the voice of an unrelated character named Cassie Rice in the animated serial Dreamland, and continuing to do voice work for Big Finish Productions in 2010.
- Jenny was played by Georgia Moffett, the daughter of Peter Davison, who played the Fifth Doctor. Moffett had auditioned for several other roles on the series, including Rose Tyler, and had also performed in a Doctor Who Big Finish Productions audio drama, Red Dawn, alongside her father in 2000. Tenth Doctor actor David Tennant met Georgia Moffett on the set of The Doctor's Daughter. She gave birth to their daughter, Olive, in March 2011 and married him on 30 December 2011.
- In the Tenth Doctor's flashbacks during Journey's End, Jenny's death is emphasised by being the only one that has its original sound clip attached: the sound of the shot that "killed" her.