From what I understand, and we won't know until it is released, the "Final Cut" is essentially a director's cut of the game. It'll have some new scenes, some scenes removed, and others will be reworked. Basically what they did for the opening a while back, just for the whole game. Supposedly this will also include some updated graphics and such, probably courtesy of the newer version of the engine. My hope is they fix some of the inconsistent dialogue.
None of that was promised in the kickstarter, which is probably why they needed a bit of a boost from a publisher to get it done.
However, the final cut is also supposed to include all the unfulfilled in-game rewards as well, of which there are a few. It's a shame we had to wait for everything, but I'm sure RTG has their reasons for waiting.