Miis collected through StreetPassing become a "unit" that can be used in the dungeons. Each progress and attack made will carry over to the next time you enter Find Mii. If you StreetPass with the same person multiple times, that person's Mii will level up and become stronger. Also, the shirt color of your collected Mii units corresponds to the type of magic they use. Below are each magic type followed by their effects:
Summon a "wandering hero".
Next hero will gain extra power (level doubled)
New heroes that enter will get a morale boost.
Heroes are "full of daring" and less likely to be scared.
Burning flames (does extra damage against blue ghosts).
Sandstorm (lowers the chance of getting scared) and allows damage against enemies holding a yellow shield.
Poisons an enemy.
Attacks with water.
Puts all enemies to sleep. Increases the number of extra attacks by a random amount.
Clears dark rooms, and eliminates the effects of black magic. Deals damage to enemies weak to white magic at 3x level.