“Sleep the night away” means that you are going to sleep. That refers to the fact that after you go to sleep, you usually wake up in the morning, which is no longer night.
Basically it is an idiom. There are great phrases you can relate too in this book: Dic of american idioms/phrsal verbs. It basically can take on any meaning the reader might have in mind. Personally, I understand it means relax.
Sleep, only to discover it’s the next morning you wake up to.