As an adult, I like texting because it is a to-the-point method to get out one-way messages/reminders like "Practice is cancelled tonight because of the weather" or "Scout meeting will be at the park instead of the meeting hall this week". Getting that information via text is much less intrusive into whatever I happen to be doing at the time than taking calls from coaches/scout leaders/other parents.
From a kid/teen's perspective, it is no different than going into the bedroom to make phone calls. When I was a kid we still had a corded phone, so I'd stretch that thing to it's limit and hog the half-bath to have some privacy. Our first a cordless phone was the Best. Thing. Ever. because I could go in my room to talk without wondering if my mom or brother were listing to my side of the conversation (not that the conversation was even very personal, but you know how teens are

).
Texting is that same basic thing, taken to the nth degree - no one can overhear, no matter where the conversation takes place, and for teens who think who they crush on and the latest hot gossip should be as carefully guarded as state secrets, there's bound to be immense appeal in that aspect of texting.