Martial law is when the National Guard and/or Armed Forces are called upon by a Governor or President to restore order when the problem is too big for local law enforcement authorities.
If there is excessive violence and civil disorder in a certain place that the police are unable to cope with, the governor or president or mayor, may call for the national guard or army to quell the disturbances. The military usually declares a state of martial law. In this situation, a curfew is put in place, looters may be shot on sight if need be. Break the military law and you will be tried by a military court in most cases. This is a most extreme solution to an insurrection or revolution.
Martial law is not going to happen and it didn't even happen during Hurricane Katrina in New Orleans. I worked New Orleans during Katrina and Martial Law was never declared. Sometimes it is necessary but it's not a threat to the American people. Remember, police officers are tax paying citizens with families also. They are not robots and they can think for themselves. It's not going to happen.