It's the anime mega-hit of... well, all time. It's currently the highest-grossing anime film ever, whether or not you adjust for inflation. (Coming after it is Ghibli, Ghibli and Ghibli.) It went big worldwide. Unsurprisingly it's good, but don't go in expecting a transcendent experience or anything. That kind of expectation could squash any film. It's a surprisingly simple story, once you've got past a couple of genre premises. It's about a boy and a girl.
Mitsuha is a schoolgirl in a rural town where there's not much to do. She's the daughter of the town mayor (who you'll eventually decide needs firing, preferably from a cannon) and a traditional shrine maiden, thanks to her grandmother. Every so often she has to participate in rituals like making kuchikamizake (literally "mouth chewed sake"), which I'd expect only perverts to drink.
Taki is a schoolboy in Tokyo, where he works part-time in a restaurant.
They're about to start body-swapping. Neither has any idea why and it's never explained.
This isn't a new idea, of course, but this film's take on it is understated and likeable. It's funny, but only in subtle ways. The animated body language is a joy to watch, for instance. The film's not going for big laughs, embarrassment comedy or anything like that. Instead it feels real. It's just two people going through something weird. What's more, body-swapping makes Mitsuha and Taki's memories go fuzzy, so it takes them a while to realise what's going on, let alone start agreeing on rules. (Those rules are never mentioned in dialogue, but you can pause the DVD and read what they've written in Japanese. "Absolutely no baths!" "Don't talk like a girl!")
Interestingly, they're both more popular with the opposite sex when they're not themselves. Neither of them is looking for romance, though.
For a while I was assuming that there wouldn't be a plot, but then to my surprise the film grew one. None of the story's individual elements are unique, but I can't remember seeing them together in this combination. It's clever, I think, especially in how some head-scratchers and/or potential plot holes resolve themselves if you think afterwards about what's been going on. Yes, I think it would work like that. The fuzzy memory is both a cause and an effect, as far as certain oddities are concerned.
Opinions differ on the music. I didn't think it was anything special, but others have felt that it's fitting and helps create the atmosphere. The art and animation, though, are beautiful, both in the big things (e.g. long scenery shots) and the details (e.g. character animation).
It's a simple story. Ignore anyone who says it's too complicated. I won't go so far as to call them idiots, but I'd be surprised to get that reaction from anyone with even a passing acquaintance with SF. You can also ignore the hype backlash, although I can understand how it came about. It's not a revolutionary film. It's not trying to change your life. It's not even trying to break the mould of Japanese youth drama. Instead it's a quiet, charming adaptation of a novel (also by Makoto Shinkai) that's building a gentle story on some interesting genre premises.