It means "I give up." Usually, you say something like this after trying to do something over and over, and not achieving your goal. This expression comes from the physical act of throwing one's hands in the air to demonstrate that a soldier is surrendering (in combat).
For example, someone asks you to guess the name of the person that he saw yesterday. You guess the names of all the people you know in common, but you are wrong each and every time. Finally, you say, "I throw my hands in the air! (I give up!) Tell me, who was it?"