First of all, do not force anything: do not try to pull it out with tweezers or push another key in on top. Keep the piece left in your hand and get in touch with us.
When a key snaps, the piece inside is usually left loose in the cylinder. With extraction tools it nearly always comes out without damage and the cylinder can still be used. If the door was left locked, it is opened once the piece is out.
Keys snap because they are worn, because the cylinder is stiff or because they were forced when turning. If the cylinder was the cause, it is worth checking or changing it so it does not happen again.
See also what to do with a key broken in the lock and our broken key extraction service.