Literally, it means you have turned over and looked beneath every possible stone. Idiomatically, it means you've looked everywhere you could and have done everything you could to try to solve some problem.
Dev: Didn't you find my book yet?
Ted: Believe me, I've left no stone unturned and did't find it.

("Leaving No Stone Unturned" example)
by AgentFire October 3, 2010