A two-party system is a pattern of party competition in which two large parties dominate elections and government, and smaller parties rarely win power. It is the normal shape of politics in the United States and in some other democracies that elect one representative per district, and political scientists have long argued about how much the rules cause it and how much the voters do.
Most democracies have five, six, or a dozen parties that matter. The United States has two, and has had roughly the same two since before the telephone. Third parties appear, gather millions of votes, and vanish, leaving barely a trace in Congress. This is strange enough that a French scholar built a famous rule around it: where each district elects a single winner, two parties tend to swallow everyone else. But Canada and Britain use the same rule and keep more parties alive. So the two-party habit is real, and it is powerful, and it is not quite a law.