The word polyamory, according to this FAQ page maintained by writer and sex educator Franklin Veaux, "is based on the Greek and Latin for 'many loves' (literally, poly many + amor love). A polyamorous person is someone who has or is open to having more than one romantic relationship at a time, with the knowledge and consent of all their partners."
(Polyamory, then, isn't to be confused with polygyny, when one man has several wives, or polyandry, when one woman has several husbands.)