I enjoyed Ancillary Justice quite a lot, although not as much as the hype made me think I would (which is, obviously, not the book's fault).
The book follows Breq, a character who used to be the Justice of Toren, an enormous space warship with thousands of ancillaries, human bodies robbed of personality and turned into avatars for the ship AI. Some calamitous event has stripped Breq of her thousands of extra bodies, the ship she embodies and the crew she once looked after, and left her stranded in a single ancillary body. Part of the book, told in flashback, concerns how Justice of Toren became Breq; part of it, told in the present, concerns her quest for revenge.
I think what I enjoyed about Ancillary Justice was the fact that Leckie takes pains to imagine a human culture that is sufficiently alien. Justice of Toren was a ship serving the Imperial Radch, a society based on expansion and annexation, conquering inhabited planets, with all the suffering and appropriation that entails. The book never shies away from the unpleasantness of its main characters, the murder they make possible in the name of "civilisation". But Ancillary Justice is not, as a novel such as, say, Isaac Asimov's similarly imperial Foundation is, a story in which humans are the same in space as they are on Earth, today. The Radchaai language, for example, doesn't differentiate between genders; the default for all Radch citizens is female (even if they're biologically male). It's interesting that the internet (read: the Puppies) has made such a fuss about this, because it's not really the point of the book; it's a detail, a reminder that we are exploring alien skies. The meat of the book really lies in its exploration of Radch politics, its conversations about the nature of power and consciousness and the interfaces between cultures.
The irony about Ancillary Justice and the Puppies, really, is that this is essentially exactly the kind of book they claim the Hugos exclude: military SF full of blood and violence and upheaval and even some slightly skeevy science. I wouldn't call it groundbreaking - or, at least, I wouldn't if sexism weren't so deeply ground into us all that we're surprised when a novel treats all its characters as female until proven otherwise. I enjoyed reading it, but it didn't make my head explode with awesomeness as apparently it did to the rest of the internet.
I will probably read the next one, though.