Once you get past the slightly differently-colored Aero theme in Windows 7, you'll realize that it looks, UI-wise, almost the same as Vista. That is, until you look down at the Taskbar. Now that's new.
First, you'll notice that the Quick Launch Bar (the little tray on the left in XP and Vista where you can click to launch apps) has been combined with the Taskbar (the place where open apps used to sit so you can access them). Now, it's just one bar of icons that opens up "in place", much like OS X's dock. You then can right click on these and pin them to to the Taskbar (again, like the Dock) so you can launch these apps when not in use.
If you have apps grouped, you can CTRL + click to cycle between windows, or SHIFT + click to launch a completely new "instance" of the program. Having two instances of Firefox open means that if one window crashes, it won't affect the pages open in another window. (Chrome already has this built in to its tab scheme, in case you were curious.)
Then there's Jumplists, which are like shortcuts for each app. By default (if you have the option of having Windows "store and display recently opened items in the Star menu and the task bar") a right click will display a list of recently opened files and websites for each app. For IE, it'll be your history, for Word, it'll be the last few docs. You can also pin your own stuff into the Jumplist. For example, if you access the same folders in Windows Explorer over and over, you can right-click drag a folder onto the Win Explorer icon and it'll be "pinned" there for easy right-click access.
Microsoft also added a fantastic timesaver by allowing you to launch the first five apps in your Taskbar by hitting the Windows Button + 1~5, corresponding to each respective program. Once they're launched, you can switch between them with the same Win + # keystroke, making jumping between your favorite apps super easy.
Even features that were present in Vista—mousing over an app to see a thumbnail preview—have been improved. Now, when you have three Firefox windows open grouped under the same icon, Aero Peek will pop them all up and you can cycle through all three, previewing each quickly. For "supported" apps like IE, it'll even break out the different tabs for you to preview. See it in action below.