At first Anderson is the captain of your ship ( the Normady ) but, he ends up giving you command of the ship.
Anderson was at first an operative for the alliance and was even a canidate for being the first human specture. Anderson helps you through the Mass Effect series. He can either become a Councilor or an Admiral. When a repear invasion heads towards earth he stays behind to aid the humans there and becomes the leader of the resistance. By the last mission of Mass Effect 3 he dies and may tell you how much of an honor it was to fight by your side.