An introductory clause used by our more urbanized compadres to abbreviate stating how something makes the person feel, for example, "I am upset that he cheated on the test" would just be "that he cheated."
Wilson: "that this nigga just hit me up for a booty call when I done told his ass if he call me again, Imma chop his motherfuckin balls off."
1 used to refer to a person, object, idea, etc. that is separated from the speaker by space or time:
2 used to refer to something that has been mentioned or was involved earlier, or to something that is already known about:
1 I've never liked that cousin of hers.
Who's that? Is that the girl you told me about?
How much are those shoes?
formal His handwriting is like that (= the writing) of a much younger child.
2 Where's that pen (= the one I was using earlier) gone?
She lives in that house at the end of Jeremy's street (= you know which one I mean).