The world classes (first, second, and third) have no official definition, but are often times used to describe the economic position of a state. The differences between the classes has less to do with the economic well being of the nation, and more to do with the geopolitical divides that emerged during and after the cold war.
First world is generally defined as a western style state that is usually capitalist and democratic, which has a high standard of living.
See also: second world and third world.
First world countries include: The United States of America, Britain, Canada, Germany, France, Belgium, etc.