What's the appeal? The idea that anyone can create an elaborate world and see it being played in and enjoyed without having to go through the troubles of development or publishing or whatnot. And because it doesn't have the restrictions many computer programs have, the potential for exciting or tense situations is infinite. Also, because it (the playing and acting, not the actual game) takes place in reality there's more potential for fun and tense diplomatic situations, because the player and the DM or even different players can say what their characters are saying, and it is literally identical to a real-life negotiation, unlike what many simulations can provide. Not only is it fun, but it is a social event, so even the reclusive people have an opportunity to interact with others. It can help with decision-making skills because of the many, many decisions to be made during gameplay. It can help with speaking skills, because very often does a situation arise in which a player must act out what his or her character is saying; this way reclusive people who are drawn to the game can gain experience in public speaking on a smaller scale and with friends, which makes it easier when they are required to do so in front of strangers. It is heavy in mathematics, so the game never feels like a mindless story-game, basic math skills are being reinforced, and players can gradually speed up their logical skills due to the constant need to add up many dice values in situations where speed is beneficial to the game.
Mostly, though, it's just plain fun.
