Imagine trying to play a video game with your eyes closed, using only a friend who whispers what's happening. To do well, you would build a picture in your head: where things are, how they move, what happens if you press a button. That picture is a world model — a small imagined copy of the real thing, kept inside a mind so it can guess what comes next before it actually happens.
People do this constantly without noticing. You know that if you let go of a cup, it falls. You know a friend will probably laugh at a joke before you finish telling it. A world model is what lets a machine do the same: hold a compressed sense of "how things work" so it can imagine forward, instead of only reacting to what is in front of it right now.