They're using the word "conscious" to mean "awake". People experience dreams; that's consciousness. They even remember them; though that's not necessary for consciousness. If no one remembered having dreams, we wouldn't be talking about them now.

It might be possible that dreams are never conscious: It would be possible to have a dream, not experience it at the time because you're not conscious, but have all the memories of it created, "remember" it later when you wake up, and experience it for the first time retrospectively, along with the illusion that you had been conscious at the time it happened.