He creepily stalked the companions of the Doctor's fourth incarnation on the eve of the Doctor's death. They became scared of him and always fled from him if they saw him, but were made to swear by a Time Lord mercenary that they would not tell the Doctor about the Watcher. When the Doctor did at last die, as he regenerated, the Watcher merged with him to complete his regeneration.
It seems, from the accounts of Ay Jay Pee Taylor and eye witness reports, that the Watcher was in fact an alternate form of the Doctor who was sent back in time by his dischordal regeneration to lead the Doctor up to his death, to ensure that time was preserved. However, even this evidence is shaky.
The Watcher himself never actually refers to himself by that name, it is simply the name that the Doctor's companions gave him. However, oddly, every else seemed to call him that too. He bears a resemblence to Slendy-Wendy Woo.