You'll have more time for taking in the few dinner shows they have available and trying some of the restaurants you'd normally not get a chance to visit.
You could also spend some time exploring Fort Wilderness, visiting the petting zoo, maybe riding the horses, or just hanging out. They also run a nightly movie and they make smores. You can either bring your own supplies or buy them there.
I hear a lot of people talking about visiting the various resorts, but I can't say that I've ever done it.
You're also able to enjoy the pools at your resort a little more. Head to the parks in the AM, then back to your resort for midday breaks. Once you're refreshed, you can tackle the parks again in the evening.
You can rent boats, schedule fishing trips, go skiing, and enjoy the water mice if any of that appeals to you. You can also go for a bike ride.
There are also various tours you can schedule.
That's about all I can think of right off the top of my head, but I know there are many other options if you don't like any of these.