Valeyard is an alternate future version of the Doctor that existed between his 12th and final incarnation. He was all the darkness and evil of the Doctor.
Basically in the 6th Doctor's second season they tried an experiment to boost ratings by having it be one 14 episode long serial: The Trial of a Time Lord. It was really a bunch of random episodes with courtroom sequences serving as a framing device. The Valeyard was the prosecutor until the Master revealed it was all a trick to get the Doctor's remaining lives (and in doing so become "real"). It was a crappy season that almost killed the show, but the Valeyard as a concept is pretty good. It'd even be neat if they had a former Doctor playing him (like he tried to regenerate and it sort of worked but aged his new body).

Bow ties are coool.