Anthropological science fiction is science fiction that primarily looks at alien cultures. While there are probably spaceships and fancy technology involved, the main point is to explore how aliens live, and to highlight the conflicts that come from humans trying to interact with an alien culture.
Star Trek liked to highlight culture clash, although this was fairly ham-handed and based more on holding a mirror up to current Earth politics than alien anthropology. Alan Dean Foster's Nor Crystal Tears (and much of the rest of the Humanx Commonwealth series), much of Orson Scott Card Ender's Game series (most especially Speaker for the Dead), and even Larry Niven and Jerry Pournelle's The Mote in God's Eye would qualify. More recently, Andy Weir's novel Project Hail Mary and Sue Burke's Semiosis certainly qualify as core examples.
As with any branch of science fiction, the edges, and perhaps even the central concept, are a bit blurry. Project Hail Mary is a first contact novel between two individuals, but clearly meets criteria. Becky Chambers' Galactic Commons series (perhaps better recognized as the The Long Way to a Small, Angry Planet series) is very much anthropology light in the spirit of Star Trek... but still probably qualifies, as differences between alien cultures take center stage. Ann Leckie's Ancillary Justice introduced the reader to a very alien and very human AI culture, in which the reader takes the role of the anthropologist trying to understand the alien viewpoint. Sarah Brooks' The Cautious Traveller's Guide to the Wastelands is a work of historical fantasy, but is also about a clash of cultures... as indeed, are many fantasy novels.
While many of these examples may make an anthropologist cringe, they are an attempt at building new cultures to show to the reader, and often do a good job at making sense of different viewpoints, building complex social systems very different from our own, and making these cultures a leading part of the narrative. When done well, these are often satisfying on a level that classic 'weird alien looks scary' science fiction can't match.