Русско-англо-русский юридический словарь

A majority government is a government formed by a governing party that has an absolute majority of seats in the legislature or parliament in a parliamentary system. This is as opposed to a minority government, where the largest party in a legislature only has a plurality of seats. A majority government is usually assured of having its legislation passed and rarely, if ever, has to fear being defeated in parliament. (Definitions.net)

A minority government is where the government doesn’t have more than half the seats in parliament and therefore can’t pass laws without the votes of parties not participating in the government. (The Independent)