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)

POTENTIAL theories
Although what the Hybrid actually was or even who was never depicted, there were four main theories that arose:
 * A Dalek-Time Lord hybrid
 * A human-Mire hybrid (Me)
 * A human-Time Lord hybrid (The Doctor)
 * The combination of a human and a Time Lord (Clara and the Doctor)

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 during Series 7.