According to most people, a stupid phrase that means the opposite of what's intended.
According to a few people, a sarcastic way to say you really couldn't care less.
Probably what was originally intended is a phrase like "I could give a shit," just a little more subtle than "I don't give a shit." Or "I could give a damn." So they could care less, but they still don't care.
Melissa: But we have to hurry back or we'll miss the final of American Idol!
Sam: I could care less about that, just as long as we don't miss Glee!