There were 5 Istari (wizards) sent to Middle Earth, and their clothes had different colours. 2 blue, a brown one (Radagast the Brown), a white (Saruman) and a grey wizard, which was Gandalf. After the battle with the Balrog he returned to Middle Earth as Gandalf the White (and he wears white clothes then) and sais "I am Saruman as he should be" (or something similar, don't have the book lying before me right now). Since Saruman is a traitor he cannot be the head of the White Council anymore, so Gandalf becomes the white Istari.
I hope my explanation is right, if there are errors please tell me! But that's what I think is the reason...
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