UI = User Interface, Dumbledork.
Basically, anything you click on the game screen that's not part of the world realm (action bars, menus, bags, map, character profile, other addons, etc).
Basically, if you look at those pictures already posted, you can see how instead of just one action bar in the bottom left hand corner, both posters have modified their UIs to have various smaller action bars in the center. One of them has his as circular icons instead of square icons. And there's lots of other things they have different.
The purpose is generally to minimize the amount of screen space used by current UI so the screen isn't as cluttered, and/or improve accessibility of certain action bars/buttons because you don't want to keybind everything. Think Feng Shui, I guess.
They're pretty good to use if you're not lazy about having to mess around with them since you have to move a lot of stuff around to make a comfortable UI. Sad thing is that when you hunt for them, most tend to have very bad screenshot examples. They almost never show screenshots without cluttering the screen with -other- addons, so it can be very hard to tell what change to the UI came from that specific addon and what came from others. And most don't very clearly describe what you can change, so it's hard to specifically hunt for one that does something you want.
I like bartender, which is what I use, but still wish I could change some other stuff. Bartender doesn't really affect the chat interface, and I -hate- the blizzard default. It has a very specific definition of where the scroll arrows show up depending on where on the screen you move it to, and the scroll arrows hang a bit to the side of the screen too, which I think often looks awkward when trying to rearrange my UI.
