Apparently we're getting THREE X-Men movies in 2018 (according to Wikipedia): "New Mutants," "Deadpool 2," and "X-Men: Dark Phoenix." Which makes this year's release of one lonely film seem awfully restrained.
The movie is set in 2029: Logan (old, tired, and not healing nearly as fast as he used to) is working as a limo driver in Texas, crossing the border to Mexico most days where he and Caliban are keeping a somewhat senile but still very dangerous Charles Xavier cooped up and drugged (to control the fits he has that can injure or even kill anyone within a few hundred metres). There are no new mutants, and almost all of the old ones are dead. But a young girl comes to Logan and Charles: a young mutant girl, very similar to Logan, and being hunted by some very unpleasant people. The three of them flee.
No explanation is given or association made between Caliban's appearance in "X-Men: Apocalypse" and this movie, and the two don't make sense together if you've seen both - but retconning is just a way of life for Marvel movies. Just my perpetual whinge about Marvel's retconning - no one else seems particularly bothered by it.
The movie deserves some credit for not laying out the entire back-story in huge chunks of exposition at the beginning: you just have to accept the way things are and wait for the details to come (some of them never will). And it's a very dark story. My final assessment is that it's quite good ... and I'm unlikely to ever watch it again because it's so depressing.