He is the head of the state. Similar separations of offices exist in other countries. The Weimar constitution did give the President a lot of powers, for instance, to declare a state of emergency and to take any emergency measures he deems necessary. This was a loophole that was exploited by Hitler.
The successor of the that constitution removed almost all remaining powers from the President. This is a mostly representative role these days with very little freedom for making decisions. Most of his tasks (appointing the Chancellor and Ministers, signing laws etc.) are strictly mandated by the constitution. The only exception I know is that he may call the "Bundesverfassungsgericht" (special court ruling on matters related to the constitution) before signing a law if there are serious doubts about the law being in accordance with the constitution.