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1.
An expression that is used to add emphasis on any comment that someone else made, usually one with a humorous intent or used in celebration. Used at the end of a comment.
Example 1:

David: Yo Mike you're an ugly fuck!

Ben: Boii !

Example 2:

Yvonne: OMG we have a snow day tomorrow! Boii !
by Ron Burgundy is the tits January 28, 2011
 
2.
A word used by the stereotypical chav in either an online conversation or via text message as an alternative to the word 'boy'.
There is no REAL reason why they use the word 'boii', but the two i's (ii) seem to be pretty popular among the chavs in the 14-18 age group.

There are other words such as

daii (day)
doiin (doing)
iino (i know)
musiic (music)

Whats worse, is that some people use the word 'boi', Message to the people who say 'boi', this doesnt make you one of those lazy typers, as its the SAME amount of words as 'boy', it just makes you look stupid.
Grace: rarrtii dat boii woz buff
Meaning: That boy was attractive
by Giorgio Enziano April 20, 2008