This word derives from the English word emotive, which is a term which is applied to modern music of a certain genre, and folks who adhere to that genre's strictures. Think 'goth', or 'metal': it's a similar use of language.
For those of us born before 1985, it may help to examine 'emo' if we produce an equation to describe it, which I formulate thus:
(Morrissey - glib wit) + .5(New Kids On The Block - assaultively high-end production) = <insert emo band's name here>
fabulous (adj.): a very few.