The ghostly figure of the Watcher had a white, featureless, unformed face and body and white clothes. Though he used the Doctor's TARDIS later, he apparently had the power to traverse time and space without external aid. (TV: Logopolis)
He was first seen silently observing events on Earth, particularly the events leading to Tegan Jovanka entering the Doctor's TARDIS. It was around this time that the Doctor first noticed the Watcher.
Although apparently silent, the Watcher was capable of communication. He communicated with the Fourth Doctor (and was seen apparently carrying on a conversation of some sorts, though what was said is unknown) and, later, his companionAdric. The Watcher, apparently on his own accord, transported Nyssa from Traken, a planet which would soon die in the entropy wave, to Logopolis and safety. Later, apparently working on the Doctor's instructions, he piloted the TARDIS from Logopolis to keep Adric, Nyssa and Tegan safe. It was during this voyage that the Watcher engaged Adric in a private conversation.
At the moment of the Fourth Doctor's death, the Watcher appeared and merged with the Doctor to create the Doctor's next incarnation. (TV: Logopolis)
In the novelisation of Logopolis, the fact that the Watcher was the Doctor was indirectly alluded to during the TARDIS scenes where Nyssa and Adric were being taken away from Logopolis by the Watcher, allegedly at the Doctor's request. While the Watcher was never heard to speak on-screen, the novelisation suggests that Adric and Nyssa could hear him, possibly by telepathy. Both of them find the voice familiar, but are unsure why they recognise it. When Adric tries to remember the Watcher's voice, he finds he can only recall the Doctor speaking.
The nature of the Watcher's conversations with the Doctor and Adric was never revealed. Logopolis suggests that the Doctor was made aware of his impending regeneration due to his statement "It's the end, but the moment has been prepared for." The knowledge passed to Adric is never revealed, although after the transformation, Adric does show an unexpected knowledge of regeneration in Castrovalva.
Several other "partial Doctors" have appeared in the history of the series, most notably an evil manifestation, the Valeyard.
The Watcher of the Doctor's old friend Rallon appeared in Divided Loyalties, merging with the Celestial Toymaker – who had possessed Rallon's body for his own – after Rallon's death to keep the Toymaker in check in future, the transition from Rallon to his Watcher causing the Toymaker's personality to change as though he himself had regenerated. This Watcher was known as the Observer.
A figure suggested to be the Watcher appeared in Renaissance. After Romana returned to Gallifrey from the Axis, the Watcher was seen lingering around the Capitol, shortly before Romana's regeneration after her fatal exposure to the Eye of Harmony. However, it was later revealed in Ascension, that this occurred in the Matrix, and her regeneration was negated when she was extracted from the Matrix.
Some fans have speculated that the character of The Curator, who appeared at the end of The Day of the Doctor, is a splinter of the Fourth Doctor, who doesn't know how he came to be (although The Moment might be behind this, indirectly or not), and relays information concerning the painting and Gallifrey's survival, before departing to fuse back with the Fourth Doctor. As with other related theories, it is neither right nor wrong, thus it should not be taken as the absolute truth to the matter.