Hilbert's Hotel is a thought experiment that illustrates the concept of infinity in mathematics. It describes a hypothetical hotel with an infinite number of rooms, all of which are occupied. Despite being full, the hotel can still accommodate new guests by moving each current guest from room n to room n+1, freeing up room 1 for a new arrival. This paradox highlights the counterintuitive properties of infinite sets. Even when a set appears full, it can still have room for more elements. David Hilbert, a German mathematician, introduced this concept to demonstrate the peculiarities of infinity and challenge our understanding of size and space.