I used the wrong name, it's BootMii, not ModMii. ModMii I believe is an automated package for Windows that will build up your memory card for modding purposes. BootMii is basically a form of bricking protection.
So if you have an older Wii, you can install BootMii in the "boot2" sector, allowing you to access backup/restore options before you even start booting the primary Wii functions. This is where you would restore the NAND if something goes wrong.
The NAND is basically the entirety of the Wii's internal memory. It's where all your purchases are stored, your save games, WiiWare games, even the amount of points you have left on the shop. Lose that, and you lose everything, unless you talk to Nintendo. And, if you're modded, there might be a chance they won't help you.
If you don't have an older system that allows boot2 access, then you can still install BootMii as a channel / software, but it doesn't protect against your System Menu going completely screwy, just if you manage to inject a WAD wrong or something like that. In that case, it's remarkably useful, although I've never had to use it.