[Informal] It means, basically, "OK, do whatever you want; I don't care". It implies that the speaker made some attempt (perhaps small) to get the listener to do something; it's not generally something you say out of the blue. It's a pretty common idiom in US English.
♂ : I don't think I'll come to the party tonight. ♀ : All right, suit yourself.
♣ Movie The polar express (2004)
Conductor : If I were you, I would think about climbing on board. (The boy hesitated and stepped back) Conductor : Suit yourself.
