Reality check - Any process by which you check if you are dreaming. The reason these work is that they exploit natural inconsistencies of the "real world" and dreams. The proverbial "pinch me" doesn't work, because you can indeed feel pain in dreams. However, by exploiting things like the stability of dreams, reality checks are very good. For example, text and numbers change frequently in dreams. Check your watch several times, in a dream, the numbers will change each time you look at it, or change while you are looking at it.

Do any type of reality check you want. Think about your mental state. Is it dreamlike? This often does not work, as in your dream you will feel like you are awake and thus conclude that you are indeed awake. Do things like breathe through a pinched nose, put your finger through your hand, draw a neon ring on your palm, check a watch, clock, or read some text over.

In regards to its necessity, it depends on the method that you are shooting for. In a reality check method for inducing lucid dreams, of course that is what you are going to want to do. However some methods like WILD don't require this (though some people prefer to do a reality check once they get into their WILD). It's all about your preference and if it works for you.