Probably less than Amazon does.
According to what I've seen they track when you go in and out of the park, when you go in and out of the hotel, and which Disney restaurants you dine at.
Clearly it's a commercial thing so they can pitch you deals on hotels, travel packages, meal packages, etc.
Before this they had a meal plan card for you, a hotel swipe card for you, and a ticket that was read by an electronic reader.
Probably the biggest piece of new information they're getting is what time you leave the park - which they had probably already been calculating from the time your card swiped in your hotel room door.
Actually it tracks where you go inside the park. Say you go on a ride that takes you photo. The band will tell Disney where you are on the ride and they will send you the ride photo for potential purchase. Also Disney Cast Members will receive information about say if you are there for a special reason and act appropiately.