The story is very simple and not much happened. There is a misunderstanding, some lies told to protect the royals, and later one of the visitors decides to live with the natives. The main appeal of the book is the poetic way the culture of the natives is described. There is also some prophecy that supposedly one of the anthropologists unwittingly aided in fulfilling, but I never really understood how.
The cat-eyed hominids of the planet have six races that serve the seventh, called royals. The royals are nearly sterile and have only a short time that their organs function, so they mate with as many peasants as they can, hoping to collect any offspring of royal quality later. Suicide among the aged seems to be the normal way to die. Afterwards, they are grieved for by professionals. The art and music of the culture seems to revolve almost exclusively around this grieving.