The term "for the sake of argument" is used by lawyers in the context of "assuming arguendo." By this a lawyer is not admitting any facts, but simply assuming that certain facts were true just for the sake of furthering an argument. For example, assuming arguendo that the court finds our party, defendant, negligent, the Plaintiff cannot recover any damages as he was contributorily negligent. With this the attorney wants to put forth the argument that the Plaintiff was contributorily negligent even if we assume that the defendant was negligent. Thus, the Plaintiff cannot recover any damages. It is assuming that the facts were as the Plaintiff contends; but the Plaintiff cannot prevail on this assumption of the defendant. The facts as the other party contends may not be essentially true. "For the sake of argument" allows one to discuss the consequences of considering the facts as the other party contends is true and thus put forward an argument.
This is most commonly used in appellate briefs.