The difference between unicameral and bicameral is that a unicameral system has one chamber and a bicameral system employs two chambers, according to Dictionary Reference. These terms generally refer to judicial or legislative chambers, but most commonly the legislative type. For example, the United States has a bicameral legislature, with the House of Representatives and the Senate each serving as a separate chamber.
"Cameral" means chamber, "uni" means one and "bi" means two. In the early days of the United States, great debate arose over representation. The Virginia Plan called for a unicameral legislature where representation depended on population, but the New Jersey Plan called for the same number of representatives per state. Roger Sherman proposed a compromise with a bicameral legislature, one chamber of which had representation by population and the other chamber had equal representation. The compromise was approved.
Despite debates on the topic from time to time, all states in the United States have bicameral legislatures in their state governments with the exception of Nebraska, which has a unicameral legislature. Many governments around the world also favor unicameral legislatures, including Canada, Mexico, Switzerland, Germany, South Africa, Brazil and Austria.
Advantages of a bicameral legislature are the ability of one house to check and balance the other and the existence of a stronger legislative branch in general. The advantage of a unicameral legislature is that the legislative branch is less likely to get mired down in details and become ineffective.