Openly having, or being open to, more than one loving relationship at a time, with everyone's knowledge and consent.
Polyamory isn't cheating with better PR, and it isn't the same as an open relationship. The load-bearing word is consent: everybody knows, everybody agreed, nobody is being managed behind a curtain. "Open relationship" usually points at sex outside a primary couple; polyamory points at the possibility of full-blown love and commitment with more than one person. Related but not synonyms.
The most common misconception is that it's a euphemism for a man with a harem, or a permanent free-for-all. In practice it's the opposite of frictionless: polyamory tends to run on an almost unglamorous amount of talking, calendars, and emotional admin. The community even coined "compersion" — joy at your partner's joy with someone else — precisely because the feeling needed a name and the language of jealousy couldn't supply one.
How it actually shows up ranges widely: a hierarchy with a "primary" partner and others, or deliberately non-hierarchical setups where no relationship outranks another; closed "polyfidelitous" groups; or solo polyamory, where someone stays their own anchor. The word is an umbrella, not a rulebook — which is exactly why people inside it argue about what counts.