Coming to Terms with Death
It is revealed quite early on in the film that both Logan and Professor X are near their deaths. In Logan's case, the adamantium that has been grafted to his body is poisoning him, thus limiting his powers and slowly killing him. In Professor X's case, he is having devastating neurological episodes which, left uncontrolled, could kill hundreds of thousand of people - including himself.
Logan deals with how these two men live their lives knowing that they will soon die. Ultimately, the two die doing what they were meant to - and always - have done: saving poor and disenfranchised and at-risk people from evil people.
Coming to Terms with Your Past
At its core, Logan is a film primarily about a man (Logan) who has to come to turn with its past as a man, soldier, and perhaps most importantly, as a member of the X-Men. Throughout the film, Logan finds old comic books that chronicled his history in the X-Men. Many people in the film thought the comic books weren't real; Logan knew that they were real. The comic books told the truth, and because he found them, he is forced to think about them and by proxy, his past.
Science
At the start of the film, it is revealed that no mutants have been born in over 25 years. It is because of science that mutants have once again begun to reappear in the world. In particular, a company called Alkali-Transigen has created a whole host of mutants - one of whom is Laura, who is Logan's daughter. Ultimately, it is because of science that most of the characters in the film exist - from Logan himself to Laura.
