It's really an abbreviation of "What say you?"...basically meaning "Don't you agree?"...or, as Quizmonkey suggests, "Innit?" It has been used thus since the 1700s.
Same as a canadian saying "eh?" at the end of a sentence I think.
"Good day for hunting eh?"
My father will add "no?" to the end of almost every sentence/statement. (He is serbian)
"Is good day for hunting, no?"
I did have a professor once who said "what?" after each sentence. It made his lectures very hard to follow, because I didn't know if he was asking a question or giving a statement. I haven't heard anyone use it since, but most if not all of my friends are common.
Another similar way of endimng a statement if one was posh was "Dontcherknow?" Now, if one isn't posh, the usual is "you know" at inappropriate points in the sentence.
Hassan, a Frenchman might say 'n'est-ce pas?', which means 'isn't it so?' but in effect means the same as your father does... basically, all these things mean 'don't you agree?', which is a polite way of turning a flat statement into an invitation to a conversation.
as well as all the above answers, the sound 'wat'/'what' was an intrinsic part of English metrical composition from at least the time of the writing of Beowulf; it was used (sometimes with drums) at the end of verses to give the effect of 'What ho' or 'Agreed'. These were quite masculine chants so maybe that is why women are not perceived as using the term as much as men...?
I wonder whether anyone has ever actually heard anyone saying any of these things, or whether they are myths, like every Irishman saying "Begorrah" or every Scotsman saying "Hoots mon"? Some of the speech patterns of the idle rich are attributable to the writings of P G Wodehouse, dontcherknow?