My very first comment-driven post! Courtsey of Alison Scott, who asks, very sensibly, "why do we call Bejewelled, Freecell and Tetris casual games, when so many people play them for hours on end?"
The basic reason for the term "casual" in this context is that it was coined by people who see themselves as serious gamers, don't like the other kind(s) of play, and wanted a way to separate themselves from all that icky other stuff. Cooties, really. In practice, a "serious" gamer is one who plays a game that calls for sustained effort, ideally both in overall play time and in the time you have to put in at a particular session to really get anywhere. If the game requires ten thousand hours total play time of successful effort and you really need three or four hours at a sitting to advance anything significant about your play status, by golly, that's mighty serious. A game that's actually done in ten or thirty minutes, why, that can't be serious at all. That's just...just...casual.
What the people who coined "casual" as a pejorative term didn't realize is that a fair number of those they targeted liked the idea of not being identified as failed hardcore players but as something else altogether. "Casual" came to be a term of self-approval for those wanting to distinguish gaming as an activity they may engage in a lot but that they can set aside when other things call from gaming as a lifestyle, a major source of self-identification. Alternative labels constantly float up out of the ongoing exchange of views in gaming forums, but so far nothing else seems close to sticking.
At its heart, then, "casual" play is any kind of play you can do a lot of (and very often the designers and publishers will be very happy if you actually do), but that you don't have to do a lot of in order to get a satisfactorily good time.
In tabletop play (whether roleplaying games, wargames, board games, or what have you), casual play is partly about ease of setup and partly about the time it takes in play to achieve neat results. In computer games, it's partly about the complexity of the challenges, partly about the precision required to complete them, and partly about the amount of repetition required once you can complete them to make overall progress. The dream design of those who love making "casual" games would require minutes or less to set up, and have both rewarding conclusions within a few minutes' play and the possibility of longer-term satisfactions from ongoing effort. I hear folks are still looking for the Holy Grail, El Dorado, and anything of value in the Oak Island money pit, too, of course.
[Image credit: Carpenter/Library of Congress via pingnews. Korea, circa 1910-1920.]