The time differential was an aspect of multiple points in a single timeline which had come into contact with one another.
When a human met him or herself from another point on his or her own timeline, the Blinovitch Limitation Effect meant that physical contact between the two versions of the person would short out the time differential between them, and could result in a dangerous energy discharge. (DW: Mawdryn Undead, Father's Day)
While multiple incarnations of the same Time Lord encountering one another did not experience this dangerous effect (DW: The Three Doctors), their proximity would still short out the time differential between their different points on their timeline. As a result, the earlier incarnation or incarnations would appear of a greater physical age than they should have, an otherwise harmless effect which would snap back once the incarnations parted ways and the time differential was no longer shorted out. (DW: Time Crash)
When time itself became stuck and began dying as a result of River Song altering a fixed point in time by refusing to kill the Eleventh Doctor, multiple points in Earth's timeline came into contact with each other as a result. The only way to repair the damage to time was for River and the Doctor to physically touch; as their personal timelines were the polar opposite points of the distortion, their contact shorted out the distortion's own time differential. This enabled them to restore the fixed point, and repair the damage. (DW: The Wedding of River Song)
Behind the scenes
The concept of "shorting out the time differential" was taken from Mawdryn Undead by Steven Moffat to finally put an on-screen explanation to the unavoidable fact that the elder Doctors in multi-Doctor stories such as Time Crash appeared older than when they had last appeared on-screen, the off-screen reason being that the actors had simply grown older since leaving the role.