Answer:
The advantage of martial law is that it grants extraordinary power to some executive (whether the President, general, or whomever is in charge) which enables him to do whatever is necessary to deal with some terrible emergency, without any hindrance from a legal system, a legislature or judiciary. Of course, we have legal systems in place to protect us from abuse by dictatorial or arbitrary rulers, so when martial law is declared, all kinds of abuse may (and often does) result. Martial law does make it easier to deal with an emergency (particularly if it is a really desperate emergency which threatens the survival of the nation in question) but it also comes at a very high cost, and it is often invoked for the wrong reasons.