Yes, your Wii needs to be connected to the internet in some way. Once you have the mingle setting on you Mii will mingle with other peoples Mii's, as long as their's is set on mingle. I think it goes by location but I could be wrong, either way your Mii wanders around to other Wii's and vice versa. It's kind of a cool function. Connect to the web if you wanna try it. I think you'd enjoy the other online functions of a Wii either way. Like the Opera browser, where you can surf the internet with your WiiMote, that's what i call the wii controller, and other games and things.
Good Luck!