From Ancient Greek “polloí,” meaning “many,” and the Latin “amor,” meaning “love.” Polyamory is the modern term used to describe the practice of romantic relationships with more than one partner at the same time, with the informed consent of all partners involved.
Polyamory is not necessarily a form of marriage, but a lifestyle. When discussing polyamory in the Christian/ Latter Day Saint framework, the term likely refers to a group marriage. Some that believe Joseph Smith Jr. was a polygamist understand his form of polygamy to be polyamory as he allegedly married other men's wives.
Some in the polyamorous community do not like including polygamy or polygamists in their understanding of this term, especially those that see polyamory as open relationships, and not as marriages or sacred unions. This is a cultural understanding, not shared by all that involve themselves in this practice.
See Doctrines of the Saints 17a-e; see also Polygamy.