It seems to have become fashionable to say something like, "You've got to represent." Another example might be, "The team really represents for the college." What's behind this? I suppose this usage makes sense if the object is understood, but the verb seems to take on a different meaning for the speaker. "You've got to show your pride" might be closer to what is meant.
"represent" is (perhaps 'was' is more accurate) a trendy slang term in the US, particularly from rap music. You can find endless examples of usage by googling rap lyrics (including various product simply called "represent").
(I wouldn't say it's "fashionable" any more - it's out of date.)
I'm sure the first usages of this could be traced, but you're asking
... WHY ...
it became a slang term.
I'd say it's really difficult to guess at "why" a given slang term, stuck. Answers could include..
a famous usage of the slang term in question, perhaps in a film
the word or topic is a popular one with a "need" for the word in question
It's possible that in this particular case, someone can point to an original "famous usage". But (as with "oblidee-oblidah" with the Beatles), usually that's just someone popularising in a hit song a term that was already prevalent among a certain group.
I'd say an interesting phenomenon in US slang and particularly rap slang, is the notion of co-opting a 'fancy', 'establishment' word and using it your own way.
So, I doubt if anyone can really answer the "why", but this term definitely fits in that pattern. Rap language (and US slang generally) likes to take fancy words, "20 dollar words" - words with an establishment or even military feel - and re-use them for their own "street" uses.
(Just BTW, on the aspect that this word is now rather old-fashioned and not trendy anymore, it can now be used sarcastically to, uh, represent an old-fashioned, lame rap scene ... I don't represent no colors, I represent my lil' sisters and brothers.)