Idris

Idris was a humanoid woman who was used as a host for the matrix, or consciousness, of the Doctor's TARDIS.

As Idris
On the asteroid inhabited by House, Idris lived with fellow humanoids Uncle and Auntie and an Ood called Nephew. Unlike the others, she was never "repaired" by House. Nephew (under House's orders) drained Idris of her mind and soul in preparation for the arrival of a Time Lord, the Eleventh Doctor. House then removed the matrix from the Doctor's TARDIS and placed it inside Idris' body. At this point, though her body was still intact, Idris essentially died; although House later referred to the TARDIS by the name Idris, there was no obvious indication any of her consciousness survived after Nephew drained her. (TV: The Doctor's Wife)

As the TARDIS
When the Doctor, along with Amy Pond and Rory Williams, exited the then-dead TARDIS to investigate why the matrix had vanished, they were quickly spotted by Idris. She now housed the soul of the Doctor's TARDIS. Idris began manically calling the Doctor "my thief" and tried introducing herself properly as the TARDIS, but could not remember what the words were. She was quickly followed by Uncle, Auntie and Nephew, who tried to keep Idris away from them by lying about her being insane. After biting the Doctor, Idris told the travellers two things: Petrichor meant the smell of dust after raining and the "little boxes" will make the Doctor angry. When told to get some rest, Idris asked if there was an off switch and instantly fell asleep, before being carried away by Nephew. She was locked away in a small cell.

After regaining consciousness, she began rambling random things that she would later say to the Doctor and his companions until noticing that the Doctor was no longer with her; she then called out to him. Following his discovery of the hypercubes House had been using to trap Time Lords, the Doctor released her. She then explained that House eats residual artron energy from TARDISes. As she was the last TARDIS, House possessed her former shell and fled to search for more food, with Amy and Rory trapped inside.

Idris later watched with the Doctor as Auntie and Uncle died. When the Doctor asked her if she had a name of her own, she responded that the Doctor called her "Sexy". Idris realised that her body was too weak to house the TARDIS' matrix, and she had under an hour left to live.

Eventually they agreed to rebuild a makeshift TARDIS from a "graveyard" of the other dead TARDIS, while they bonded. Idris then infused the mechanical bits with a part of the TARDIS' inherent energy to allow them to follow House. The Doctor had Idris send a telepathic message to Amy with details on how to get to a backup control-room and lower the shields; having been told by the Doctor to send a message to "the pretty one", Idris sent the message to Rory, much to his chagrin.

When they got the shield down, the new console landed on Nephew and blasted him into atoms. The Doctor quickly introduced Amy and Rory to Idris. Idris collapsed, close to the end of her life. The Doctor tricked House into transporting them into the main control room. The Doctor pretended to congratulate House for defeating them.

When Idris died the matrix was released inside the control room and merged back with the TARDIS. It proceeded to purge House from the TARDIS in a battle of souls that House couldn't win. With the last of her energy, the matrix used Idris's body to tell the Doctor that, although she would always be there for him, this was the only occasion when they could talk, using her last moments with a voice to say the word she never got to say to him when he first left Gallifrey: "Hello. Hello, Doctor. It's so very, very nice to meet you." As the body burnt up, the TARDIS whispered a quiet "I love you", after which the Doctor was left to wipe a tear from his eyes.

Idris, when about to die, kept repeating into Rory's ear, "The only water in the forest is the river," adding "Some day you're going to need to know that." (TV: The Doctor's Wife)

Personality
Little was known of Idris‘ original personality. She expressed fear before her imminent demise and most likely suffered years of abuse just to entertain House.

Once the Tardis inhabited Idris’ body, she was confused and seemingly delusional, incessantly muttering phrases and subjects that had happened or were going to happen due to possessing a non linear grasp of time. This caused the Doctor to think she was insane at first. Once she adjusted, Idris demonstrated great loyalty and attachment to the Doctor, helping him rescue his companions and tearfully saying goodbye once Idris’ body expired. (TV: The Doctor's Wife)

Abilities
Once the TARDIS inhabited Idris' body, she retained a non linear grasp of time due to normally being a time traveling vessel. This allowed her to foresee things that had not happened yet and to give useful advice to the Doctor and Amy about future events.

Being made of the artron energy that powered TARDISes, Idris was capable of releasing large amounts of it from her body and transferring it into another recipient. She used this ability to power the Junk TARDIS, forming a shield around it and enabling it to take off. (TV: The Doctor's Wife)

Behind the scenes

 * On his blog, Neil Gaiman stated that Idris arrived on the asteroid because she came through the Rift. He also said that she was in a Victorian party dress because she had been to a Victorian party.
 * Idris' appearance is also reminiscent of the Bride of Frankenstein, from the ; both the TARDIS and the Bride are "artificial" beings inhabiting a body that originally belonged to other people.