TL;DR version is that TvTropes suddenly and without warning changed their policy, claiming that all user-submitted material was their intellectual property, despite, if I remember correctly, changing such a policy like that nullifies it. This caused a break, were somebody decided to pull as much as they could from the TvTropes servers and used that to found AllTheTropes - something that might have been illegal, although it's difficult to say since what TvTropes did was illegal too.
At least, that's how I read it as.
Actually, ATT has subsequently reconstructed everything without using any material directly copied from TVT (or so they claim).
There was also the issue of censorship. The official line from TVT was that it was imposed by Google with the threat of ads being pulled. IIRC it originated with people from SA trolling TVT by sending advertisers screenshots with their ads on pages with borderline sexual content, but there's been SJW undertones for years. The advertising shitstorm gave an excuse for a lot of the crappy mods and admins to start banning dissenters while also affording the SJW types a chance to push for heavier censorship.
It's honestly sad, considering that it was a (somewhat shit) joke site that is now being run by a cabal of morons who take it completely seriously. That, and the way it subtly encourages dull, cliched writing and thought--if you think that potholing a link to a trope page is interesting or deep, there might not be much left to save. That's not really the fault of the abusive mods or pro-censorship crowd, though.
But yes, those two factors combined are why it was forked, and why the fork is both completely reliant on donation to stay afloat (Orain was, incidentally, a charity service that hosted wikis for free), as well as why ATT is very specific about the type of license they operate under. Just your friendly neighborhood jerk reminding you now that TVT is run by assholes for assholes these days.