Technically, I got my hands on New Super Mario Bros. U twice, because you can play it both with the Wiimote and also the GamePad. So I had to make sure I had both experiences... even if I was terrible at both sides, what with it being a platformer and everything!
With the Wiimote, you just keep running to the right to keep up with the constantly moving game world, jumping to stay alive. However, the player with the GamePad can actually help you out by placing platforms for you to help you make more difficult jumps. The GamePad displays the exact same screen as the TV, so it's easy to just tap with the stylus and create platforms in just the right place. Of course, as the pace increases, things get hectic, and overwhelming, especially if you've got more than one player on screen. While you're helping Mario, Luigi could be falling to his doom! (You can have up to five players at a time, one GamePad and four Wiimotes.)
The player with the GamePad can also tap to keep stuff from falling on Mario, like spiked blocks. Only the smaller ones, though, not the big ones! They can also tap enemies to stun them and make it easier for Mario to defeat them or breeze past. Although after you fill the star meter, you can take out enemies for Mario.
You can play single player, but then you won't have any help getting through the levels. They're clearly designed to be able to be beaten by just one person, but with secret areas up high or down low that you'd only be able to reach with the help of an assistant making extra platforms for you. (Oh, and you can only have four on screen at once, so you have to keep that in mind as the earlier ones will disappear if you make more!) And in single player, you can even play New Super Mario Bros. U on the GamePad screen instead of the TV.
Having someone helping to create extra platforms does make things slightly easier, because you're less worried about falling to your death. However, communication is key. I would think that if you had some people in a good rhythm where they knew what they were doing, it would be a lot of fun. But at a press event with all the noise, and none of us knowing how to play the game that well, the whole thing quickly degenerated into chaotic fun. I did watch someone play farther, and even encounter some boss battles, which was good, because playing it myself, I certainly wasn't going to see any of that! But Nintendo has found a really clever way to use the Wii U GamePad to add a new wrinkle of gameplay to the traditional Mario platforming!