An one-party system is a form of government where the country is ruled by a single political party, meaning only one political party exists and the forming of other political parties is forbidden.
Some countries have many political parties that exist, but only one that can by law be in control. This is called a one-party dominant state. In this case opposition parties against the dominant ruling party are allowed, but have no real chance of gaining power. For example, in China all power is vested in the Communist Party of China. Other parties are allowed to exist only if they accept the leading role of the Communist Party.