Regenerative dissonance was a mental illness seen in Time Lords. It occurred when the personalities of a Time Lord's previous incarnations lived on inside the body of their current incarnation, exerting just as much influence on the body as the personality of the current incarnation. Time Lords known to suffer from this illness often committed suicide as they couldn't cope with the voices. (AUDIO: World of Damnation)
The Time Lord calling himself the Eleven by their eleventh incarnation suffered from this. (AUDIO: The Eleven) Other than him, the Time Lord who lasted the longest with this condition shot out both his hearts with a staser in his eighth body. (AUDIO: World of Damnation)
The regenerative dissonance altered the nature of the energy released by the afflicted Time Lord when they regenerated, with the result that they were essentially immune to the Ravenous, a race who essentially fed on regenerative energy. When the Nine and the Eleven briefly met, their two versions of the Four actually argued about the Nine's current plan, prompting the Eleven to observe that it would appear that regeneration actually affected the past personalities as well, speculating that they 'filtered' their perception of their past selves through their current persona. (AUDIO: The Odds Against) It would appear that the condition essentially manifested a copy of the old personalities rather than just allowing them to remain 'active' on some level, as the Eleven found himself talking to the Eleven in his subconscious after he was shot by the Masters but before he actually regenerated into the Twelve (AUDIO: Day of the Master).
Neural inhibitors allowed users with regenerative dissonance to maintain control over the different personalities within their mind. The High Council gave the Twelve one as she went on a mission for them. (AUDIO: Planet of the Ogrons)