The movie is set in something vaguely resembling the British Victorian era, uses stop-motion animation just like "Paranorman" (with which it shares the production company Laika), and is about a young boy trying to save his friends from persecution and death.
Eggs (named because of the box he wears, and voiced by Isaac Hempstead-Wright - Bran Stark of "Game of Thrones" fame) is a boy raised from a baby by the underground dwelling boxtrolls, who come up into the town above at night to scavenge mechanical parts for their inventions. Archibald Snatcher (Ben Kingsley), an unpleasant man who wants to better his social standing, convinces the town that the boxtrolls steal and eat babies, and sets out to round up and kill all of them with a promise of social advancement from the mayor. The boxtrolls don't fight back because they're just goofy and sweet, so the task of defending them falls to Eggs - who has no familiarity with human society. Fortunately, he falls in with the mayor's daughter (Elle Fanning). Laika has laid out a lot of jokes for adults, but you'll have to pay serious attention as a lot of them flash by as names on businesses and boxes ... and be prepared for an endless string of cheese jokes, many of which the kids won't get (although there's plenty for them here).
I wasn't too keen on the style of animation. Even the cutest characters had a slight touch of the grotesque in them - I suppose that was true in "Paranorman" as well, but I thought it worked better in that one, with it being about zombies and raising the dead and all. Plenty cute and reasonably funny, it's not a bad film, but I don't think I'll be watching it again - unlike "Paranorman," which is a story of surprising depth (and with better fitted animation) that I've watched several times.