Polyamory hasn't really hit the dictionaries yet and the people who practice it are still endlessly hobnobbing about its exact definition and parameters; there is some vigorous infighting on some issues (notably the endless swinger controversy), and there may always be. So any pat summation I offer here is actually a moderately aggressive move, an attempt to subvert the public eye to my particular agenda on the subject. But I'm not above that.
The Greek roots underlying the term (coined by one Morning Glory Zell in 1979--I've done my homework on that one, though I know rival claims exist, usually vague ones) give you an idea what it's about: multiple loves. Polyamory is often, maybe mostly, defined as "responsible non-monogamy," which pleases me by its clarity and its broadness. (Most of the time, I think, differently worded definitions still boil down to about the same thing, though there are divergent definitions out there--which generally seek to narrow the term's meaning by excluding a class or two of undersirables, if you want my take on it.)
Responsible non-monogamy. The point really is the departure from monogamy, but since almost everybody in the world has already departed from their professed monogamy--secretly and dishonestly--the "responsible" had to be moved to front and center to emphasize the differences between conscientious poly and the indiscriminate quest for more nookie.
I started questioning the nature of love, which rapidly led to questioning monogamy, at the age of fifteen. Importantly, at that age I could easily have believed that I would be unwillingly celibate for life, which means I was thinking about these ideas in a practical vacuum. For better and for worse; certainly I had no sense of societal subtleties at all, but on the other hand any real and present girlfriend would most likely have quashed the whole line of questioning instantly, setting me back by years.
There are a zillion ways to look at the question, a multitude of arguments, and it's tough to choose which to bring up when you're just setting the stage. To sum up, I might point out that nobody expects your old friend to be cast aside every time you make a new friend. But then maybe you'd say, that's different, and I'd say it really isn't, and we wouldn't be able to talk about it much until I found out why you think it's different, and since this is the web you'd have to to explain. Alternatively, I might argue that jealousy gains me nothing in particular (since I don't care about propagating my genes) while polyamory fills my life with beautiful people and widely varied perspectives. Or, to make the single quickest statement I have on the subject, I could say: I just don't see why sexuality should be a special case in human interactions.
For the longer explanation (but not the agonizingly longwinded all-inclusive ramble) I think this is a reasonably tight overview of poly and mono: they are two compromises, opposite compromises, between basic and unreconcilable human desires: jealousy and libido.
All else being equal, it is to our genes' advantage that we seize as many mates as we can manage (and yes, that applies to females too--the limit of one offspring at a time only slows it down a bit), so it shouldn't surprise anybody if we all tend to want all the likely mates in sight. At the same time, it is also to any individual's genetic advantage to have mates who refrain from shopping around themselves--male and female both--so it should surprise nobody that we feel an emotional drive to constrain our mates to just such a behavior.
In a population, these urges will sort themselves out in one of several ways. We can't all mate with lots of people and keep them all exclusively. Perhaps one set of people, or particularly one sex, might succeed, having exclusive access to many mates. In fact this is probably the most common outcome, so that the stronger sex simply wins; in species where males are bigger, they'll fight among themselves for harems of females, and where the females are bigger, they'll command the favors of all the males. Monogamy only becomes an issue within species who have little or no sexual dimorphism.
With the interesting exception of our own. Any other primate with a 4:5 mass ratio between females and males would simply be a unimale polygyny--which, in fact, is just what most human societies have been. But the remaining societies have experimented with a riot of other arrangements, and a prominent few, of course, have been sticking with monogamy for centuries. Why? Presumably--and this is a bit more speculative than the rest of what I've been spouting here--out of a sense of fairness. Monogamy is a compromise: any committed party limits his or her libido to a single chosen mate, and in return, the other partner does the same, so the jealous desire of each party to secure the other's exclusivity is satisfied. Nobody has to waste energy raising some dumb kid with none of his own genes; nobody has to be afraid her mate and his services will be drawn away by a rival. In theory, anyway.
Polyamory, in its simplest form, is a very similar compromise, just reversed: jealousy is given up so that libido may be freely satisfied for all parties involved. In practice, lots of safeguards are generally in place for the participants' physical and emotional security--advance notice, maybe, or even asking permission--stringent safe-sex practices--all manner of negotiated agreements and that sort of thing. But the essence of it is simply the voluntary abdication of jealousy, with the attendant payoff of reclaiming libido.
There are so many more ways to look at it... if you think I ought to talk about more of them here. Or click here to get some other points of reference. For now, that's enough out of me, I think.