There are two experiences you remember as dreams. The first is a creation of your mind and sunconscious about what is currently going on in your head. This I would say is not real to the extent that it is an illusion. (Philosophically this can be argued, but I'm here to make my second point.)
It is a regular occurance that your spirit leaves your body while you sleep and visits other places, other people, other worlds other dimensions. This is a real experience but it is so surreal and since most people are not taught this, they natural assume these odd experiences are also dreams. But they are nit. It is this ability. Sonetimes called astral projection, that allows people to have insights into the future, connect with others, have inspiration, and beconomic aware of things thing they could not possibly know unless they were connecred somehow. This is real, you probably call it a dream, but it's not. So I suppose dreams are not real, but what you think was a dream may have been real.