From here: http://forum.wordreference.com/showthread.php?t=2095473 Meaning 1: I say: I think it's going to rain tonight. You say: How can it rain? There isn't a cloud in the sky. I say: You've got me there. [=Your argument is better than mine.] Meaning 2: I say: Mr Jones isn't at his desk You ask: Where is he? I say: You've got me there. [=I don't know the answer to that.]

You've got me there means that you've asked a question that the other person can't answer. John: How do I do this homework? Do you understand it? Mike: You've got me there, I have no idea.