Anarchy in C-evo is similar to the concept in other Civ-series games: a state between proper governments, either by design during a revolution or after a capture while a city recovers. Anarchy lasts for three turns, during which each affected city's units need no support and buildings need no maintenance. You cannot sell buildings or "home" units in any city that is enduring anarchy, nor can any other nation engage in diplomacy with you when your whole nation is in anarchy. The on-screen Manual describes it at the bottom of the "Government Forms" page.