The Hybrid
The Hybrid was a legend on the planet Gallifrey telling of a creature thought to be crossbred from two warrior races — the Time Lords and the Daleks — according to prophecies from the Matrix. Rassilon was searching for information about the Hybrid as according to the legend it would stand over the ruins of Gallifrey before proceeding to unravel the Web of Time. (TV: Hell Bent)
References
Davros attempted to transform some of his Daleks into Time Lord hybrids by granting them regeneration energy taken from the Twelfth Doctor, intending to fulfil an ancient Gallifreyan prophecy which warned of a Dalek-Time Lord Hybrid that would conquer Gallifrey. (TV: The Witch's Familiar) However, the Doctor later claimed the Daleks would never allow anything to be half-Dalek and that the hybrid of Time Lord prophecy was "Me". (TV: Heaven Sent) When Ashildr became immortal after being given a Mire repair kit, the Doctor mentioned that there was "a little piece of alien inside of her, so in a way ... she's a hybrid". (TV: The Girl Who Died) In the Cloisters at the end of the universe, the Doctor declared that Ashildr, who at that point went by "Me", was the Hybrid, at which point she countered with the theory that either he singly was the half-Human Hybrid or that if the Hybrid could be interpreted as being more than one being, then the Hybrid could refer to the pair of the Doctor and his companion Clara Oswald. Just prior to losing his memories of Clara, the Doctor indicated that his reckless actions in trying to prevent her death made him the Hybrid. (TV: Hell Bent)
The author of the Time Lord Academy textbook on Gallifreyan history thought that the Doctor was bluffing about being the Hybrid, and the Hybrid was never going to be half-Dalek. He proposed other candidates: a splicing of Human and Mire; a girl part-Human and part-wolf; and two girls half-human and half-Time Lord, one made Lord through metacrisis, the other conceived in the Vortex. None of them quite fit into the prophecy, though. (PROSE: A Brief History of Time Lords)
Behind the scenes
Although Hell Bent, among other series 9 episodes, offered multiple possibilities as to the identity/nature of the Hybrid, showrunner Steven Moffat, in an interview for Doctor Who Magazine #504, confirmed that the Hybrid referred to the pairing of the Doctor and Clara, and retroactively linked this fact to the reason why the Doctor's TARDIS exhibited some hostility towards Clara in series 7. (This would also explain the hearts the Hybrid would break; the hearts would belong to the audience.)
