There is no single definition of polyamory, but the consensus among people who study and/or practice it seems to be that polyamory is “honest, open, responsible non-monogamy” that involves being open to more than one simultaneous romantic, intimate, or deep emotional relationship (these are usually but not always expressed sexually), and in which all parties have full knowledge of the arrangements and participate of their own free choice.
In this context, deep can mean emotionally intense, or it could also mean the kind of depth that comes from knowing someone for a very long time, and having learned to trust them implicitly; there may not be intense feelings about this person all the time, but you know they have your back, and you can count on them to be there for you.
They are the people that you think of as a permanent part of your intentional family.
There are other kinds of relationship that can constitute part of a polyamorous situation, such as a peer relationship with someone you feel bonded to, that you take into account when you are making life plans, and who you have deep emotional sharing with—but for whatever reason, it is not a sexual relationship.
Usually, we do not think of certain kinds of relationships as being part of polyamory: swinging, casual “pick-up” sex, true seduction, “friends with benefits” where the benefits are the main part of the friendship, and many other arrangements where the main purpose of the connection is the sex.
We aren’t passing any judgment on any of these arrangements, and we support any fully consensual choices that individuals make about their sex lives, but these are not what is usually meant by “polyamory”.