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)

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.)