Father of Time

The Father of Time, or simply Time, was an impossibly powerful humanoid being of Gallifreyan lore, who identified himself as the one who had kept watch over Time itself before the inception of the earliest Time Lords. He once made the first six incarnations of the Doctor go through an ordeal he called "the Test of Time", shaping the Doctor's destiny in the process; at the end of this adventure, the First Doctor recognised the Father of Time as a future incarnation of himself.

Nature
When explaining his nature to Susan Foreman, Time explained that "before the oldest of Time Lords existed, there was only Time himself". As he put the six first Doctors through his Test, Time demonstrated a number of abilities beyond those of a normal Time Lord, beginning with his first appearing within the First Doctor's TARDIS control room in the form of a hourglass which rapidly grew in size and exploded into his slightly-translucent humanoid form.

Nevertheless, just before he was sent back to his own time by the Father of Time to face the Zarbi, the First Doctor caught a glimpse of Time's attire beneath his robes, which included the Doctor's scarf, The Doctor's recorder and a stick of celery, and suddenly wondered just WHO he was. (COMIC: The Test of Time)

Origins
Just before the First Doctor was sent back to his adventure with the Zarbi, he caught a glimpse of the Father's attire underneath his pale flowing robes, which heavily suggested to him that Time was his own future self somehow. When depositing the Doctor and Susan at 76 Totter's Lane, Time knew that he was sending them to "a new life".

Time himself told Susan Foreman that he, Time, existed before the inception of the Time Lords, hence his now wanting to test one of the beings who had named themselves after him.

At any rate, he was known to the First Doctor by reputation before their meeting, with the Doctor recognising him as "the Father of Time" on sight. (COMIC: The Test of Time)

The first Test
Deciding to test the Doctor, the Father of Time appeared to the First Doctor and Susan Foreman while the Doctor's TARDIS was stationed in deep space on 16 August, 1963. Materialising first as a strange hourglass, and then in his humanoid form, in the TARDIS control console, the Father explained his nature and his intent before remotely sending the TARDIS to Skaro in its "unforeseeable future", namely minutes before its final destruction. He guided the First Doctor and Susan as a disembodied voice as they wandered outside, carefully not revealing to them the name of the creatures of this planet, (COMIC: The Test of Time) whom they would only meet properly some time later. (TV: The Daleks)

When the two tried to flee the natural catastrophe they encountered by getting back into the TARDIS, the Father disabled the ship's dimensional transcendentalism, making it just as small inside as outside, and warned them that such an escape route would have been "too easy". Though initially distraught, the First Doctor passed this phase of the Test, understanding that he and Susan must use one of the Daleks' lifts to ride out the storm at the very heart of the planet as Skaro was torn apart. Satisfied, Time put them both back in the TARDIS, which he drove to materialise at 76 Totter's Lane, in front of I.M. Foreman's junkyard, and told them that they would find "a new life" here while he set the stage for the next Test. (COMIC: The Test of Time)

The Final Test
The Father of Time once again spoke to the First Doctor as a disembodied voice while the Doctor was facing a Zarbi with Ian and Barbara, warning him that the Final Test was underway. The Doctor vanished from Vortis and found himself staring at Time's impassive face on the TARDIS scanner screen: he was inside his own TARDIS's console room, where he found his five next incarnations, whom the Father had "plucked" out of their timelines. The Father of Time explained that he had incapacitated the TARDIS by disassembling the control console; if the Doctors did not regain control of their ship soon, the Ship would collide with the heart of the Sun.

Understanding that the disassembled console was a red herring, the First Doctor reminded his other selves of the power they held as Time Lords, which would allow them to turn back time within the TARDIS using their sheer force of will, and thereby reverse the Ship's deadly course. Once more, the Father of Time spoke as a disembodied voice, announcing that the Doctor had passed the test, and he scattered the five future Doctors back to their respective timelines.

Just before the First Doctor was sent back to Vortis, however, he caught a glimpse of the smiling Time, whose robe slid aside to reveal his attire beneath was a collection of accessories of the Doctor's across the Time Lord adventurer's many lives — with the earlier Doctor teetering over the edge of realisation before he was returned to the normal course of history and forgot. (COMIC: The Test of Time)

Behind the scenes

 * The Father of Time's identity as a future, "ascended" form of the Doctor is not elaborated upon, as it constitutes the final twist at the of the story, whose "The End" caption mysteriously reads "The End of the Beginning".
 * He is obviously distinct from the personified Time of the Virgin New Adventures, a female incarnation of Time identified as an Eternal who chose the Seventh Doctor as her Champion and was eventually revealed to also be the granddaughter of Chris Cwej.