I've not watched regularly since 2011 (since, ironically, the Jeff Hardy thing at Victory Road), but I've managed to catch a great deal of this feud and here's what I make of it:
Jeff Hardy had an "I Quit match" with Matt Hardy in which he did a super-duper ultimate Swanton Bomb from a staircase in the arena onto Matt through some tables, causing the "I Quit" match end in a no-contest because they were both fucked up and had to be carted out -- go figure.
Some time later, Jeff Hardy was attacked by Willow, which was weird (the whole feud is weird, just go with it) because Willow was actually an alter-ego created by Jeff Hardy that he wrestled in TNA as for a period of time, and yet he was being attacked by his own alter-ego somehow. And then there were MULTIPLE Willows attacking Jeff, and it was finally revealed that the main false Willow was, in fact, Matt Hardy, sporting a new, rather interesting look.
So, at that point, crux of the feud became that this super ultra special awesome Swanton that Jeff did during the "I Quit" match completely "broke" Matt Hardy. And when I say, "broke", I mean, "caused him to grow out and poof his hair and dye a streak of it blonde, call himself "Broken" Matt Hardy, refer to Jeff exclusively as "Brother Nero", and use a goofy, exaggerated EVIL~! accent he didn't have before like he was doing a bad Johnny Depp in Sweeney Todd impression".
This has resulted in god-tier acting from both Matt AND Jeff, and even Reby Sky (Matt's legit wife and mother of their child), who's appeared in some of the vignettes and is now Matt's heel valet. One such segment involved Jeff going to Matt's house to sign a contract for a match, only for Matt to lure Jeff into a barn with a wrestling ring in it (and a round wooden table, for no apparent reason at that point) to sign said contract, and then Reby pops in, pretending to throw her baby at Jeff (turns out it was a doll) as a distraction so that Matt could Side Effect Jeff through the aforementioned wooden round table (hey, there WAS a reason for that!).
Anyway, they've had some matches and some fights and the already-explained Oscar-worthy acting, and now it's all come to a head in what is being called the "Final Deletion" -- or, as Matt said it, "THA FINAAAAAL!! DAAALEEESHAAAAN!!!". By which he means, "the 'final deletion' of Jeff Hardy", because Matt's been claiming that he's been solely responsible for all of the Hardys' success in wrestling, and to that end, this "Final Deletion" match will not only take place in the Hardys' hometown of Cameron, NC, but it will also be for "control of the entire Hardy brand".
So, that's the best way I think I could sum up the feud as it's happened so far. Do yourself a favor and look up some of the segments if you can, because this is some kind of fucking wrestling fever dream.