"I already have plenty of things to read/do when my mind does need a wonder in the evening/weekend" -- for many people, especially those in their 20s who came of age using Facebook, Myspace, AIM, etc, one of those things we do to occupy our time is use the Internet to keep up with friends who we, for whatever reason, can't just call on the phone or hang out with in person. Recent college grads especially suddenly find that their once close friends are scattered across the globe; Twitter lets them maintain a sense of nearness.
To me, that's the appeal. You don't have to be unemployed to have 10 minutes a day in which to keep up, particularly when you weigh that 10 minutes spent reading Twitter against the amount of time it would take to maintain individual correspondences.