This is an analogy to playing a chess game. At the end of the game, whent he king is trapped, you are "out of moves". It means that a person has tried everything they can think of to "win" in a real-life situation, but nothing has worked. Now, they can't think of anything else to try. Ex.: "I have tried everything to keep my marriage with Jennifer together. I've cut my hours at work, helped more around the house, and tried being more romantic. I've even agreed to go to counseling. But she still wants the divorce. I don't know what else to do. I'm out of moves."