A civilian government is a government not run by the military. These governments are usually associated with democracies, though the Marxists Internet Archive points out with the selected works of Mao Tse-tung that Communist governments can also exercise civilian control.
Not every government is civilian-led. At the other end of the spectrum is a military junta, defined by Wikipedia as a group of military officials who takes over an existing government, usually by force. Even more extreme is a stratocracy where the military rules directly as the government. Civilian governments usually differ in that they have a civilian commander-in-chief who directs the military such as described in Article II of the U.S. Constitution, according to Cornell University Law School.