All I know is what I've read elsewhere, but you have asked a fair question.
As I understand it, a Hardin crimp has features of both a folded crimp and a roll crimp.
Using your example, the term pertains to (1) trimming a 2 3/4" 12 gauge case to 2 1/2", (2) loading that case as if it were a regular 2 3/4", (3) inserting a "B" wad, or .070" cardboard wad over the shot and (4) fold crimping in that "B" wad with what remains of the shortened case mouth. It is the "B" wad that retains the shot, not the shortened, folded over case mouth.
The big edge reported here is that the technique permits a standard fold-crimp style 2 3/4" 12 gauge reloading tool to be used to produce useable 2 1/2" shells without the need to fabricate extra items such as shortened crimping dies, etc. etc.
I don't know if this technique works better with certain types of cases, though you'd think that plastic might work better. -Only speculation on my part. Hope you get feedback from shooters who have actually made these up.