This is an insulting and derogatory description for somebody who is very, very cheap. It's believed that crab's asses are rather compact, so someone tighter than a crab's ass is about as selfish/cheap/greedy as it gets.
Jake: Bill by the way, what did you leave our waiter?
Bill: 15%.
Jake: Christ Bill you're tighter than a crab's ass. I have to stop eating with you if you're going to embarrass me like that again in public. That poor waiter worked his ass off you cheap fuck.