The Remake explicitly takes place in a parallel dimension, an alternate reality, to the original game. Further, this parallel timeline is being affected by the events of the main original timeline.
So it's kind of both a Remake and a Sequel.
The Planet in FFVII is literally a living entity, and creates powerful, monstrous antibodies to protect itself from harm (as a Dirge of Cerberus player, you're likely already familiar with this). The "Nomura ghosts" are another of these antibodies, similar in purpose to the Weapons, though instead of dealing with physical threats they're custodians of fate and destiny, who are deployed by the Planet to make sure that the timeline plays out as it should.
They interfere with the protagonists a number of times, down to outright attacking you several times, but seem inconsistent and sometimes they help you instead of hindering you. If you're familiar with the original plot, it pretty quickly becomes obvious that they interfere every time some ripple effect is threatening to majorly change the plot. I'd basically worked out what they were by the time the game actually outright explained it.
Somehow Sephiroth (the OG's main villain) is aware of the original timeline and is Taking Steps to change things and beat these antibodies, so he can actually win instead of being defeated. It's not made completely clear how, given you still interact with him very little (though still a hell of a lot more than you did at this point in the original game), though I expect the explanation to be revealed in the next game. Might be time travel -- Final Fantasy games obviously don't shy away from time travel as a plot device (see the very first game). Might just be as simple as him picking up 'echoes' between worlds. Who knows. Even Cloud is getting visions of the original game timeline, up to and including oblique references to Aerith's death.
There's a big confrontation at the very end where Sephiroth tries to convince Cloud to team up with him to defeat the Nomura ghosts and break destiny. Cloud rejects him, but once everyone talks it out they decide that the future they saw in the visions (Meteor, the destruction of Midgar, Aerith's death) isn't good enough and they want to break destiny anyway so they can try for a better result this time around. You defeat a giant manifestation of the Nomura ghosts and successfully destroy them, breaking destiny. You get a final boss fight against an incarnation of Sephiroth, manifested through one of the "reunion" black-cloaked figures from the original game, and it's basically like playing the final fight from Advent Children. The fight is pretty good.
At the end, the group resolves to leave Midgar and go after Sephiroth to stop him, following in the footsteps of the original timeline versions of themselves, but no longer necessarily tied to the original story, free to forge a new path ahead.
It's hard not to see the Nomura ghosts as a really heavy-handed metaphor for the expectations of the fans who just wanted a pure remake of the game with nothing changed, literally forcing you to follow the original plot slavishly even when it doesn't completely make sense. You (representing Nomura) reject this and break destiny, freeing yourself from the expectations/timeline of the original game.
It's not great, and it's far from the best thing about the Remake (that would be the Honeybee Inn sequence, which is amaaazing), but it's not so terribly done that it ruins the rest or anything. I finished the game with positive feelings and excited to see what is going to happen in the next game, given that they basically just broke the whole thing open and are free to basically do what they want now.
But yeah, controversial. Some people are going to absolutely hate it.
