Good question, we never did set up a starting point for him, like we did for everyone else.
Jet is not quite the man we knew in the show. Much like before, Azula had the renegade terrorist Jet sent to Lake Laogai as soon as he was caught. He's not the shell he was in the show; he's had a long time with this brainwashing and has developed into a full fledged person once more, however, his radical nature has been reapplied. On the surface he's very supportive of Azula's regime; he is a "true believer" in her in the way he once was with destroying the Fire Nation. However, as Earth Commons ambassador, he argues vehemently for the sake of his people. He remembers the way he once was, but he is convinced that Azula is the answer to the problems he once perceived. The worst part, of course, is that in many ways she really is. Over the years, there has been a sort of on/off thing going with Katara, as well. There is a mutual attraction like there was in the show, but Katara's motivations aren't entirely pure. She knows who he was, and wants to bring that man out again, but she has to play the long game. If she strikes too early, he'd just turn her in to Azula. She's starting to be successful, though... Jet is starting to doubt himself.
Sorry, that's a little long-winded and not exactly his role.
In short: He represents the Earth people actively where Kuei is passive. He supports Azula but something is off in his mind that he can't pinpoint yet. Katara is gradually making him aware of it. He is a tipping point; the Earth nation believes in him, far more than their king. If he can be turned, it would be a huge win for the rebels.