Chances are that we're going to get our first look at footage from Logan before the month is over, but The Wrap has a new piece up which claims to shed some light on the plot. Apparently, the movie is going to be set in 2024 and it will be by far the darkest release set in the X-Men Universe to date. That explains the R-Rating then, but will it be fun? Who knows, but it should be interesting to see if it gets the same sort of critical whipping as Batman v Superman: Dawn of Justice did back in March.
Regardless, the site goes on to reiterate some points we already know, like the fact that Wolverine is now an alcoholic, he's sick, and his powers are beginning to fade/sometimes not work at all. The girl in the poster is described as a young mutant who has two claws, and fans of the comic books will know that description lines up with X-23. In 2024, mutant births have plummetted and a new government type operation called "Transigen" is said to be turning young mutants into "killing machines."
Here's where things get really interesting though. Professor X (now quite a bit older than when we last saw him) is also not in the best of health and his powers have grown increasingly unstable. He doesn't even remember Logan at times, but the clawed mutant gets some help from Caliban, who will apparently be played by Stephen Merchant. Seeing as we actually met a version of that character in X-Men: Apocalypse, I'm not sure how that will work, but take this with a pinch of salt for now anyway.