The second baseman is the defensive player (specifically, an infielder) who covers the area of the field surrounding second base. Unlike the first baseman, he usually does not stand right at second base. Rather, he occupies the area in between first base and second base (but slightly closer to second base).
As a second baseman, your responsibilities are the following:
Since the second baseman occupies the middle of the infield, he is often in the center of the action (literally) when a baseball is hit into the field of play. He must be aware of base runners' positions, react quickly to sharply hit baseballs and throws from other fielders, and always know where to throw the baseball next. He also must be willing to move around the field, such as covering first base in certain situations or catching baseballs hit into shallow centerfield.
The second baseman is important in turning double plays. Often, another defensive player will field the baseball, then throw it to the second baseman who will touch second base to get a runner advancing from first to second out. He will then throw the baseball to the first baseman, who will touch first base to get the batter advancing to first out. If both the second baseman and the first baseman touch the base before each of the runners do, then both runners are simultaneously out. This is called a double play, and it frequently involves the second baseman.