A Multi-party system is opposed to a one-party system and a two-party system.
In a one party-system there can only be one party- this is the case for example in the case of communism.
In a two-party system there typically can be more than two parties, but in practice there are two main parties and they alternate at being in power.
In a multiple-party systems there are multiple parties, and they typically form coalitions, and new parties appear and some old ones dissapear.
