Many people seem to think that they know what fun is. However, they can only describe it. Everything they expound upon is based on the subjective feelings. They have no idea what the core reason is, which raises the question "How can you create entertainment without knowing what fun is?" Well, I believe it is absolutely necessary to know what fun is in order to create something truly amusing. Because every element within a media that is entertaining must connect to the core beliefs of fun.
Fun in its simplest form can be objectively defined as thinking. To think is to have fun. A person may wonder why when they are bored, they are thinking about something else. Sure, they are thinking, but they are not thinking about the subject matter at hand; therefore, the subject infront of them appears boring. Once they have nothing interesting to think about, they effectively become bored. If they had, they'd be daydreaming and enjoying it for the moment. "Why exactly is thinking, fun?" they might ask. Well, one way is to compare it to experiencing it; they experience it mentally rather than phsically, but since every thing people experience is based on perception, it's really all mental in any case. (Note - Really, thinking is just enjoyable by itself, think about it...) Even when people start to experience what they desire, it rarely turns out exactly as they have dreamt. Each changing event gives new information, no matter how miniscule, which pushes them to think in order to adapt to the current situation; this is exactly why they still enjoy it while experiencing what they desire--they are continually thinking. So, that only goes to show that: If their head isn’t in the game, then it’s not fun!
This core idea exists in any form of entertainment media. Movies are not entertaining if it doesn't grab interest from the viewers, which nudges the observers into caring and wondering; Comedians aren't funny if they can't get the audience to guess what's coming up next and at the same time have something that the audience can't ever think of (example: funny particular voices that people can't think up to be exactly as the result.); Games are not fun if players are not thinking about the game; etc. Any entertainment media needs to promote and invoke thinking in order to be enjoyable as well as direct the audience's attention toward itself (i.e. keep the audience engaged)...
Edit: My Big3 for fun is 1)Problem-Solving (any challenge, customization, whatever that challenges the player to think and do something) , 2) Emotion, and 3) Sensation. Emotion and Sensation put together makes an experience. That's what music, movies, etc. provides. And games are the most interactive and powerful media of them all. (Example: Shadow of the Colosus or Mario provides much more of an experience than challenge.)