There are infinitely many rooms, so it is okay even when they are all full
Imagine a hotel with rooms 1, 2, 3, ... continuing forever. Every room is occupied. Yet even when a new guest arrives, or even when an entire bus carrying infinitely many guests arrives, the hotel can accommodate them all! Try it yourself and see how.
The trick: Tell every guest, "Please move from room n to room n+1." Then room 1 becomes empty. If an infinite bus arrives, tell the guest in room n, "Please move to room 2n." Then every odd-numbered room becomes empty, so all infinitely many new guests can be accommodated.
The hotel is currently full, starting from room 1
💡 This is possible because infinity is not "a very large number" but a different kind of concept. It would be impossible in a finite hotel, but with a "countably infinite" set like the natural numbers, the whole set and some of its parts (such as only the even numbers or only the odd numbers) can be considered to have the same "size" — a strange phenomenon that happens only with infinity.