Chakotay was a member of the Maquis who's ship got sucked into the Delta Quadrant by the Caretaker array along with Voyager. His ship was destroyed there, so he and his crew decided to join with Voyager for the ride back to Earth. Janeway made Chakotay her first officer and granted him the "provisional" rank of lieutenant commander.
He was the one who recommended Torres for chief engineer. This doesn't speak well for his true loyalty to Voyager. More likely, it suggests he wanted to get the ship destroyed before they got back home. He frequently objected to Janeway's decisions, but he would turn around and tell his former Maquis crew to obey her orders anyway since she's the captain.
Chakotay and Janeway's relationship seemed to sway back and forth from teetering on romance to counter point. I guess her genocidal rampages were just too much for him. It was also implied that he had romantic relations with Seska before joining the Voyager crew. However, by the end of the series, Chakotay hooked up with Seven of Nine for no particular reason.
Chakotay embodies just about every Hollywood stereotype concerning American Indians there is. He is supposed to be Mayan, yet he pursues vision quests and believes in animal spirit guides. People use a medicine wheel and coyote stones  to try and heal him. He insists on not even scanning a burial site to avoid violating its "sanctity". Hawks are sacred symbols of his people and messengers of the spirits, etc. Just as Neelix takes every opportunity to tell stupid personal anecdotes, Chakotay is always ready with one of the "sacred legends of his people". And to make it all even worse, this was apparently all programmed into American Indian genetics by (white) alien visitors thousands of years ago.
If Voyager had gone on longer, its entirely possible the writers would have had him open a casino next to Neelix's galley.