The White Guardian, more accurately called the Guardian of Light in Time (TV: The Stones of Blood), was the anthropomorphic personification of order and good in the same way that his opposite, the Black Guardian, embodied evil and chaos.
However, different interfaces of the Guardians held different perspectives, with the Black Guardian later claiming to represent freedom while the White Guardian embodied domination. The Fifth Doctor even criticised him as the lesser of two evils, embodying the letter of the law rather than the spirit. (AUDIO: The Destroyer of Delights)
The White Guardian sent the Fourth Doctor and Romana I on a quest to find the six segments of the Key to Time, changed into a variety of forms and scattered across time and space. Assembling them, he said, would allow the restoration of balance and order by freezing all time for just a moment. He warned them of the Black Guardian, who also sought the Key. (TV: The Ribos Operation) After they had assembled the first two segments, he warned them of the Black Guardian again, as a disembodied voice. (TV: The Stones of Blood)
He was aware of the Black Guardian's plans involving Cuthbert. (AUDIO: The Pursuit of History) To stop chaos coming to the universe, he created order by causing the Salonu ship to crash and maintain the historical causal loop that created the Conglomerate. He also placed the Ecidien Cerebus Bird in the TARDIS. (AUDIO: Casualties of Time)
The White Guardian and the Black Guardian offered Enlightenment, symbolised by a crystal of unknown powers and great value, as a prize to the winner of a space race undertaken by Eternals. Turlough threw the crystal at the Black Guardian, who vanished in a burst of flames. The White Guardian explained that the Black Guardian would exist as long as he did until neither was needed any longer. (TV: Enlightenment)
On another quest to find the Key to Time, the Fifth Doctor and Abby found him in 9th century Sudan, crammed in "a measly number of dimensions small enough to count on one hand, a human hand" (as he said). He posed as the Legate of the Caliph, the embodiment of law in that era, collecting taxes and punishing tax evaders such as Lord Cassim. He was only in Sudan after he followed the TARDIS there. This was Order's way of finding the Fifth Segment of the Key to Time. His adversary and he did not trust each other to carry out the Doctor's orders and watched each other as they worked. When the Doctor left the Sudan, he was stranded there, waiting for the universe to end. (AUDIO: The Destroyer of Delights)
He remained there for so long he forgot who he was. Eventually, Zara found him and took him to Atrios, where he became Professor Lydel, the scientific adviser for Princess Astra's mission to the Chaos Pool.
Thanks to Amy and the Doctor arriving, he came in contact with the segments of the Key and was rejuvenated. He tried to take the Key from the Doctor when he assembled it, using the Teuthoidian's army, which happened to be on Chaos. He failed and was returned to the Howling Void and his eternal struggle with the Black Guardian by the Grace. (AUDIO: The Chaos Pool)
The White Guardian later sent the Seventh Doctor, Ace and Benny on a quest to find the six segments of the Key to Time, scattered across the Doctor's personal timeline when he last disassembled it. (COMIC: Time & Time Again)