The original phrase came from a song title, "Cry Me a River," and referred to someone crying so much they could fill a river with their tears. When used as an idiom, it is a sarcastic way of telling someone "you can moan and complain all day long, but you won't get any sympathy from me."
Bob: "My flight was terrible. There was an error in my reservation and I was unable to get a seat in First Class."
Fred: "Oh, cry me a river. My original flight was cancelled and I had to spend the night sitting in a chair at the airport so that I could catch the first plane heading out this morning."