What are dreams?

Well although there isn't a set in stone definition, here's the Webster Dictionary version:

Dreams are very common and it happens to everyone but theres no one way to explain the purpose of dreams.Dreams generally occur in the rapid-eye movement stage of sleep- when brain activity is high and it's closest to being awake.

During REM sleep, the eyes are constantly moving around even when the eyes are closes.
Dreams can occur during other stages of sleep but they are less vivid or memorable.

For 90-120 mins each night, every single person dreams.  Sometimes, the dreams are straightforward in their meaning to the dreamer.