HTC Sense UI is a skinned version of Android. It is designed the help bring you and your social life together, and it does just that. Very well might I add.
At first, Sense UI, or Sense can be a little confusing, because it is a whole bunch of stuff piled on top of Android. The Droid Incredible is running the newest version of Sense, which is placed upon Android 2.1. Many phones that run the newest version of Sense, have the option to completely turn off Sense, sadly you are unable to do that on the Incredible, but then again, why would you want too?
Sense improves some of the worst things about Android, it provides a wonderful, spaced out virtual keyboard, a better music player, and a better camera.
Sense also adds more widgets, plus the stock Google widgets, it adds more live wallpapers, but removes the Nexus One wallpaper. It comes with a several apps already included like Peep, FriendStream, Footprints, Quickoffice, and Teeter.