The answers so far attribute this to the Southern US. But I don't think this is an innovation in English grammar that came from there. Part of this is because it is also used in dialectical speech in the UK and Ireland. But the other reason is that it seems early modern English would often use "them" where we would now use "those".
For example, the 1662 Book of Common Prayer has
As we forgive them that trespass against us.
The King James version has, in Genesis 12:3:
And I will bless them that bless thee, and curse him that curseth thee: and in thee shall all families of the earth be blessed.
(note that they also did not write "he who curseth" either, as certain prescriptive grammarians might demand)
Shakespeare's Henry IV part I has Falstaff saying:
A plague upon such backing! Give me them that will face me.
The easiest way to find these examples is to search for "them that" (though it is not foolproof, as it can occur in present-day English in phrases with reported speech, like "Tell them that I am here"). However, I have not been able to find any examples without the "that" yet (e.g. "them apples", "them people", "them bones"). It is possible that the standard English of that era only used "them" as a demonstrative when followed by "that" (maybe someone else who knows the history of English better can answer).
However, the other answers are right on one thing. It is no longer part of standard English.