Someone who is your significant other, but whom it would be an insult to call "a boyfriend" (because it implies temporariness). "Boi" also implies a very deep bond of loyalty, almost like in a gang. A lot of goths and spooky kids use this word, often with "muh" or "tha" or "thee". I'm a little too old for that though.
Girls also use it to describe a good-looking goth or spooky kid.
That's my boi right here, and I love him to death.
If you act like that, my boi will fuck you up.
Mmmm...what a sexy goth boi! He looks like Reznor.