Well, it's not just about having a lot of money, although that doesn't hurt. Economic stability is a big factor, as well as political stability and human development. Think of it like a report card for countries - they need to score high in all these areas to make the cut.
But here's the thing: the term First World was actually coined during the Cold War, to describe countries that were allied with the United States and other Western nations. It was like a club, and if you were in it, you were considered one of the cool kids. Now, though, the term is more about economics and quality of life.