Fun is enjoyment. It's the more lighthearted aspect of the pleasure derived from a good game, the one that makes you smile. (Contrast Challenge.)
The hardcore gamer tends to equate fun with the application of hard-earned skill and sheer moxie to a difficult set of in-game decisions. That is, to him, challenge is fun. To most people, fun is something else. Game elements that can be fun for players: SillyStuff?, Humor?, Thwarting? other players, BurstsOfActivity?, Speed?, lying and Bluffing?, SocialInteraction, opportunities to be silly or creative, Surprise.
Many of these elements, when introduced in the most obvious way, work in direct opposition to NoSkillCap and, in general, making a game challenging. For example, the easiest way to add surprise to a game is to add a major random element. That detracts from strategic thinking. The easiest way to add speed is to eliminate some of the strategic information that might lead to AnalysisParalysis?. For this reason, most TableTopGame?s can be pegged as either StrategyGame?s or PartyGame?s. But the best party games are both FunAndChallenging.
The basic idea is that "fun" is what you're having when you're working on something not to hard, not to easy. That is, neither boring nor frustrating. This ties in with LearningCurve? thinking for a game. "Is the LearningCurve? too steep? Or is it just plain flat?"