I think reality is a word that can't be fully explained. This is cause one person will see it as this, and the other person will see it as that.... There is probably more then one good answer for this question. While at the same time we all have a basic agreement on what it roughly means.

Some people will say that dreams are not part of reality, others will say they are. It all just depends what reality means to you. The word "reality" has a lot of different layers attached to it, and dreaming is one of those. It's up to you what "layers" fit with your definition of reality. Hope this makes sense in a way..