I bought my friend an elephant for his room.

This joke hinges on a delightful bit of wordplay, specifically a pun that takes a common idiom and twists it literally. When someone says "Don't mention it," they usually mean "You're welcome" or "It was no trouble at all." It's a polite way to dismiss thanks. However, in the context of an actual, enormous elephant now occupying a friend's room, the phrase suddenly takes on a very literal and absurd meaning: please, for the love of all that is sensible, do not bring up the giant pachyderm currently residing indoors.

The humor also stems from the sheer absurdity of the setup. Who buys an elephant for a room, and how do they even get it in there? This creates a wonderfully bizarre image that sets the stage for the punchline's clever linguistic turn. It's a classic example of finding comedy in the unexpected literal interpretation of a phrase, playing on our expectations of everyday language and then subverting them with a giant, four-legged surprise.