The term “martial law” refers to a situation in which the civilian government of a given area loses its power and that power is given over to the military. This is why it is called “martial” law. The term is best used when discussing countries that have at least some amount of rule of law. For instance, it would be hard to talk about “martial law” in North Korea as that country is, in normal times, in a state where its government does not have to have any regard for people’s rights.
In a more democratic country, martial law exists when a government needs to suspend some degree of civil liberties and to allow the military to enforce law and order. This generally happens in extreme emergencies. For example, the New Orleans area was essentially placed under martial law after Hurricane Katrina because it was too difficult for the civilian government to protect the people who were still there. As another example, parts of the United States were placed under martial law during WWII because it was believed that there was a serious danger of Japanese attack.
Martial law is not a precise term. It simply refers to instances when civilian governments lose power or control and need to suspend civil liberties. In such cases, particularly when law and order is maintained by military troops (as opposed to police), we say an area is under martial law.