The joke comes from the infinite hotel paradox, which is from a property of infinities that you can always add to them and they’re still infinity. This leads to a paradox where if you have an infinite hotel room with no vacancies, every single room in the infinity is full, as a given. But if everybody moved over one room, there would be an empty room in position 1.

The punchline is that in real life if you asked every guest to move over 1, they wouldn’t want to, and some would be big babies for some reason.