OK I haven't played in a while, but here's the basic rundown:
Shepard is the main hero the game is based around.
Ashley is one of the main sidekicks.
I forget the name of the guy who I always kill at the end and save Ashley.
T'Soni is an alien doctor and on the side of Shepard.
Garrus is a bad ass who's an assassin type shooter.
Wrex is a frog-like beater.
Tali is the engineer genius of the group
All those guys join forces against Saren, who used to be fighting on the good side but was turned by his sentient ship. Saren has a couple mini-bosses, probably the ship itself, Matriarch Benzia, and probably another that I'm not thinking about.
The great thing about the game was the multiple dialog choices and different ways the game could play out. There were difficult choices to make at every turn. Highly recommended.