The legislative branch is the part of the United States government that creates laws.
Whenever you read about congresspeople in the Senate or House debating a law, you're reading about the legislative branch: the branch of the government that writes, debates, and passes laws. Making laws can be called legislating. The term legislative branch usually refers to the U.S. government, but there are also legislative branches on the state and city level, and there are legislative bodies all around the world, like England's Parliament. When you hear legislative branch, think "making laws."