The word "thang", used in this context, was an Ebonicism used to refer specifically to a cultural meme or norm, which those who belonged to the special group-- in this case, African-Americans, would immediately recognize and understand... whilst those not belonging to this group (whites or non-blacks) would fail to understand, appreciate, or even recognize.
Thus, by extension, a "thang" is a folkway, meme, norm, predilection, code, shibboleth, artifact or behaviour exclusive to, or closely allied with, a particular sub-group of the larger populace.
White wannabe-rapper: "Yo, what is up widdis? One jar at the end of the bar filled with pickled eggs and another one filled with pickled pig's feet? Yo, dass nasty!""
His Black buddy: "Man, it's a Black thang, you wouldn't understand."
Or, during a moment of treasured understanding:
Straight guy: "Would you mind please telling me what IS it with you gays and Barbra Streisand?
Gay guy: "Oh, I guess it's a Queer thang, you wouldn't understand."
Or, at a typical American High school:
High School Teacher A: "One of my students actually has a tattoo of a tiny black teardrop under his left eye! It's kinda creepy... What is THAT all about??"
High School Teacher B: "Yeah, well that's a Latino gang-banger thang. Supposedly it means they've offed someone."
"Lemme get two of them thangs".
"Ayo ma, why don't you gimme that thang".