It's by Makoto Shinkai, the director of 2016 international mega-hit Your Name. There are apparently some themes that to date he's used consistently throughout his work, such as distance and separation of loved ones (very much the case here), beautifully artistic backgrounds and lighting (yup) and SF and/or outer space (still true here even though the film contains no SF elements). It's a work of art. It's something to show intellectuals. However I wouldn't call it a film to show ordinary viewers, who'll probably get grumpy about the misleading anti-plot and the apparent downer ending. Most of the people in my family wouldn't like it. My father and my uncle would eat it up with a spoon, though.

Shinkai himself claims that this isn't a downer ending, incidentally, but his reasons are quite narrow and specific. Comparing this and Your Name, they feel very much like the work of the same person, but this one gives the impression of having been made by someone who's not in a good emotional place. I'd compare it to the way Neon Genesis Evangelion is very shaped by its writer/director suffering from depression. Regardless of whether or not that's an insulting and wrong armchair diagnosis (which it probably is), that's how the film felt to me. I've just dug up some Shinkai quotes:

(a) "The thing about getting rejected is that you reflect and think and analyze about why you got turned down. You learn a lot more from stories about getting rejected than stories about becoming happy. That's why I prefer those stories."

(b) "When I was growing up, I didn't have tons and tons of friends. When I was growing up and until I got married, I had some times when I felt a bit lonely and a little bit isolated. Even after I got married. Even though I have people I love right beside me, I sometimes feel lonely, and that is part of the reason why this loneliness plays a big part in my life. Maybe if I wasn't a person like that, I wouldn't have become an animator, and I wouldn't write about those things."

...whereas Your Name is more accessible to a general audience. It has a plot and a happy ending. People like buying tickets to see those things... but let's get on with talking about this film! Its subtitle is "a chain of short stories about their distance", which is all-important. A plot summary might go as follows:

EPISODE 1: "Cherry Blossom". Takaki and Akari are thirteen-year-olds and very close, but unfortunately their families move a lot for work. They're separated. They write letters to each other, but eventually discover that Takaki's family will soon be moving a very, very long way away. They'll be so far apart that they wouldn't even be able to meet up by train any more, were they to try. They make a date to meet up one last time, before this happens, which is emotional... but of course it has to end with their parting. Takaki realises that they'll never be together again and they both have one last letter they never gave each other.

EPISODE 2: "Cosmonaut". Years later, Takaki is about to graduate from high school and is choosing what to do next. University, perhaps? However there's a girl in his class who likes him. No, not Akari. Her name's Kanae Sumida. This episode is entirely from her point of view.

EPISODE 3: "5 Centimetres per Second". Years later (again), Takaki has a job in Tokyo. Akari is going to get married (not to him), while he falls into depression and quits his job. The end.

You can see how that storyline might throw a casual audience.

The likely problem is that one's normal movie-watching habits will mislead you. Ep.2 will have you wondering how the film's planning to resolve the potential love triangle, but that's a misreading of what the film's about. There's not going to be a plot resolution. You'll just tie yourself in knots if you're trying to anticipate one. This episode's about Kanae, not Takaki. She can sense the distance in him. He's coping with physical distance (from Akari), but she's the one who's grappling with her feelings and with a deeper reading of the movie's theme.

Ep.3 is the hardest to embrace, because what it's doing is the furthest from what we expect from movies. To see why Shinkai doesn't think it's a downer ending, you've got to be reading the episode in terms of the film's chosen themes and applying that fairly specific view to the protagonist's final smile.

Contrastingly, ep.1 feels the most conventional to a casual viewer. It could easily be the start of a romantic story, which at that point is how you're likely to be interpreting it.

It's delicate and beautiful. I'd definitely recommend it to anyone who likes arty, slightly esoteric movies. It's something to think about and discuss afterwards. However I definitely wouldn't recommend it to anyone who likes simple, straightforward films and blockbusters. It's sad and lonely. It's a movie where Shinkai has said that the theme is "reality", since real life doesn't always give you happy endings and love usually fails. (I'm not going to comment on that.) The good news, though, is that it's only an hour long. Two hours of this kind of mostly plot-free melancholy might have been tough going.