A reality check is exactly what it sounds like. It's an action or test you perform in order to determine whether you are dreaming or not. It will usually be something that is guaranteed to act differently when you are in a dream. If you practice doing them throughout your day, you will be able to perform them in a dream when you realize something doesn't seem right. The idea is that when you perform the RC during the dream, it will prove that you are dreaming and cause you to become lucid.

Hope that helps.