The vWii is an interesting one, for sure. To cut a long story short, when you hit that Wii Menu button, your console actually becomes a Wii. A bunch of hardware switches are flipped resulting in all the fancy Wii U hardware being disabled and everything being rearranged in such a way that, as far as any running software is concerned, the console is a Wii. The only exception to this is the three CPU cores (which can't be effectively locked out) compared to the Wii's single core, although this has proven not to be a problem. This Wii similarity runs deep, even having vWii system updates hosted on the same servers as the original Wii's. Due to this, Wii games run perfectly.
This is possible since both the Wii and the Wii U use PowerPC processors (along with an ARM security chip), which means that Nintendo doesn't need to emulate any of the number-crunching bits. They chucked the Wii's graphics card in there and everything just worked! It's a pretty nifty piece of design if you ask me.
Nintendont takes advantage of this in order to run GCN games. You may remember that early Wiis were able to run GameCube games - this is down to the same reason the Wii U can run Wii games. It's all PowerPC, and Nintendo just added parts and toggled them on and off as needed. Using this, one can run (PowerPC) GameCube games on the (PowerPC) Wii U. It's not totally cut-and-dry though - Nintendo didn't include GCN parts (such as controller ports and the graphics card) on the Wii U, so Nintendont is forced to emulate these. In this way, it's a bit of a hybrid between native and emulation - the number-crunching is native, but basically everything else is emulated. It's like the ultimate dynarec.