Polygamy
Also: polygyny, polyandry, plural marriage
Marriage to more than one spouse at once — a marital and often religious institution. It is distinct from polyamory, with which it is frequently confused: polygamy is about marriage, polyamory is about loving relationships.
Polygamy means being married to more than one person simultaneously. It usually refers to a formal, often religiously-sanctioned institution, and it most commonly takes the form of polygyny (one husband, multiple wives); the rarer reverse is polyandry (one wife, multiple husbands). Polygamy is illegal in most Western countries as a marital status, and it is historically structured around a single central spouse to whom the others are married, rather than a web of mutual relationships.
Polygamy is the term polyamory gets confused with most often, and the distinction matters. Polyamory is about loving, romantic relationships and carries no requirement of marriage; it is typically egalitarian or at least mutually-negotiated, and is not tied to any religion. Polygamy is about marriage and is frequently embedded in patriarchal or religious frameworks where the wives are not partnered with each other. 'Poly' as a prefix sits in both words but they describe different things.
The confusion is worth clearing up precisely because critics sometimes conflate the two to import polygamy's associations (coercion, patriarchy, religious control) onto polyamory. Most polyamorous people are not seeking plural marriage and would not recognise their relationships in the polygamy frame.