>>23318375Miis can arrive in your game by either Streetpass, Spotpass (friends list) or being invited. You can invite three for free once a day, repeat invites cost 10 play coins.
Every 5 miis that arrive rewards a free poké diamond (but there's a limit to how many per day, too many Miis in one day starts giving you coins instead).
Miis will appear in your stages, noted by other balloons being in the background when you are on the balloon select screen.
Miis you encounter when rescued may reward a diamond, or maybe just coins. It seems that Miis you've met a lot are much less likely to reward diamonds though, so friend code miis have limited potential against streetpass or invites.
They then serve as an escort and give potions, or X Attacks, X Defends or X Speeds. They're a nuisance to keep alive though, with pretty much no advantage to looking after them.
Up to 4 Miis will frequent your Castle Town each day. At least one will let you revisit the stage you just cleared for one, two or three diamonds depending on how many stars that stage had.
Others will let you visit certain stages for a 500 coin entrance fee. If they are late-game players this may let you access stages you do not have balloons for yet.
On rare occasion they might just give you a diamond, just for talking to them.
That's basically what Miis are good for.