This word has been known at least since the early nineties (the Usenet newsgroup alt.polyamory was formed in 1992) but hasn’t yet reached the dictionaries. It describes a way of living in which individuals have multiple relationships with the knowledge and consent of their long-term partners, without deceit. Such relationships have been described as “responsible, ethical or intentional non-monogamy” and do not necessarily involve sex, though they usually do. One form of polyamory is the open marriage and another is polyandry; there is much flexibility in arrangements.
Proponents of the lifestyle stress that though they are outside society’s norms, they adhere to well-understood codes of behaviour, and that they have little connection with “swingers” or others involved in very temporary liaisons. The word is a compound of poly- with amory, a supposed noun meaning “love” that is formed from the Latin amor, from which of course we also get the adjective amorous.
The word is much less commonly spelled polyamoury. An individual is a polyamorist and the adjective is polyamorous. The shorthand term poly is also used to describe this lifestyle or someone engaged in it.