A one-party state is a country that uses a one-party political system, 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, which 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.
Most one-party states are dictatorships. The Soviet Union from 1922-1991, Nazi Germany from 1933-1945, and the Kingdom of Italy (ruled by Benito Mussolini) from 1922-1943 are some the best known examples of one-party dictatorships in history. Some one-party dictatorships are called a police state or a military dictatorship, if a secret police force or the military is used to keep a dictator in power through force.