To me, a casual game is one that you can take up for a short period of time and progress happily without a lot of tedious leveling, as in WOW.
They can range from very easy to very challenging, and come in all types of genres. They're getting more and more sophisticated too. Frankly, I love them, just as I do adventure game in general, but casual games really fit my busy life, especially when work gets to be as hectic as usually does.