The first baseman is the defensive player (specifically, an infielder) who is stationed at first base. The first baseman in charge of fielding/catching balls that are hit in the area surrounding first base, including outside the right foul line or in shallow right field.
One of his most common plays occurs when a batter hits a ground ball, and is attempting to reach first base. Another fielder collects the baseball and throws it to the first baseman, who then catches it with his foot on the base (sometimes he will catch it while not on the base; if this is the case, he must run and touch the base). If the first baseman has possession of the baseball and touches the base before the runner does, then the runner is out.
The first baseman is often tall and a left-handed thrower. Being tall gives him an advantage so he can reach throws that fall short of first base. Being left-handed is also an advantage; since he is situated on the right edge of the field, all his throws go to his right (and it is easier to throw to the right using your left arm).
If the baseball is not automatically caught by a fielder, the first baseman is the second line of defense in preventing batters from becoming base runners. When the pitcher cannot get the batter out at home plate, the first baseman is usually the next person charged with getting him out. Many outs are made at first base, so it is important that the first baseman can catch well.