Means "Many Loves". It means having multiple commited relationships with people you are mutally in love with, and everyone wants it to be that way.
This is not to be confused with swinging or multiple relationships, where you are sleeping with the other people or they are friends with bennies, whom you love. That is called non-monogamy, and to say it is polyamory is a lie.
"I told Brad I'm in love with him, and my husband Rick is very happy for us."
"No, we're polyamorous. You can only cheat on rules that exist. We don't have an agreement to be exclusive. But an example of me cheating would be to not tell Rick that I'm in love, because the rule of honesty is right up there with the rule that the primary relationship comes first"
"I could never do that. I'm too jealous"
"Are you sleeping with both these guys?"
"Now that I'm in love with both of them, yes. But you don't have to be having sex to be polyamorous, because what it means is that you are mutually in love with more than one person at a time. Most people do sleep with those they love, but sex is not what makes you poly"