Jolee Bindo is a human Jedi who fought in the Great Sith War against Exar Kun, left the Order afterwards, and has been living alone in the Shadowlands of Kashyyyk ever since. He joins Revan's crew late in Knights of the Old Republic and spends the rest of the game refusing to behave like a Jedi Master.
The grey Jedi, before that was a cliché
Bindo predates most of the fandom vocabulary that grew up around him. He is not a "grey Jedi" in any doctrinal sense; he is an old man who watched the Council make a set of decisions about attachment that destroyed his own life, declined to keep arguing about it, and left. His refusal to lecture is the most Jedi thing about him, and the game knows it.
Function in the party
He is the only companion who is neither impressed nor threatened by what Revan turns out to be, which makes him the one person who can say the useful thing at the right moment — including his summary of why Bastila Shan was always going to be vulnerable to Malak.
Behind the scenes
Written by David Gaider and voiced by Kevin Michael Richardson. His official Databank entry once claimed he was not crucial to completing the story, which is demonstrably wrong: he is the only party member who can get past the Czerka force field on the way to a Star Map.