Martial law was the giving over of governance to the military in the event of extreme circumstances.
In 2246, Kodos declared martial law and seized control of Tarsus IV when an exotic fungus destroyed most of planet's food supply. (TOS: "The Conscience of the King")
In 2367, during the Borg's invasion of the Federation, martial law had been declared on Earth for the first time in close to a century. (DS9: "Homefront")
In 2369, while under the influence of the Saltah'na energy spheres, Major Kira Nerys offered Odo to rule the promenade under his own martial law, if he would support her "mutiny". (DS9: "Dramatis Personae")
In 2371, Kai Winn Adami suspended local government and declared martial law in the Hill Province on Bajor when Shakaar Edon gained support in this region. (DS9: "Shakaar")
Federation President Jaresh-Inyo declared martial law on Earth in 2372 when elements within Starfleet led by Admiral Leyton disabled the global power grid, apparently the prelude to a Dominion invasion. Because of this, Starfleet troops took position in all regions of the planet and fortified themselves, a measure strongly supported by Earth's population. (DS9: "Paradise Lost")