Martial law is the imposition of military rule by military authorities over designated regions on an emergency basis—usually only temporary—when the civilian government or civilian authorities fail to function effectively (e.g., maintain order and security, and provide essential services), when there are extensive riots and protests, or when the disobedience of the law becomes widespread. In most cases, military forces are deployed to quiet the crowds, to secure government buildings and key or sensitive locations, and to maintain order. Generally, military personnel replace civil authorities and perform some or all of their functions. The constitution could be suspended, and in full-scale martial law, the highest ranking military General would take over, or be installed, as the military governor or as head of the government, thus removing all power from the executive, legislative, and judicial branches of the federal government.
Typically after a disaster like the tornadoes, some people will go on looting sprees where they will take whatever they want. The police and other authorities are tied up attempting to assist their citizens. The military comes in and takes over those duties.
I hope that helps.