The Hybrid

The Hybrid was a Gallifreyan legend that said all Matrix prophecies predicted that a hybrid creature, thought to be crossbred from two warrior races, would stand over the ruins of Gallifrey and unravel the Web of Time, breaking a billion billion hearts to heal its own. Rassilon searched for information about the Hybrid. (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 he intended that the Hybrid was the pairing of the Doctor and Clara. He 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 audience's.)