A metaphor for infinity. A hotel with a single, never ending hallway.
Hilbert’s Hotel is an imaginary hotel in which there are an Infinity of rooms in a never ending hallway (or, sometimes, different configurations of hallways). One of the key concepts was that the hotel can be full, but also have room for more (infinitely more, actually) new guests. It is a construct around which an argument is made for varying “”sizes” of infinity.