What does this really mean? It means having more than one person that you love as your girlfriend/boyfriend (husband/wife/lover) at the same time. Most people are capable of this. You love your sister or brother. If you had another brother or sister would you love for each be any less?
But there is more to it than just that, the responsible side. In this day and age that has multiple meanings. If you love more than one person than each of the people involved should know about it, and be comfortable with it. Otherwise it is cheating and perhaps unsafe.
There are a number of very good resources about poly, so I am not going to try to cover it all here (check out at the links). What I am going to try to do is define and discuss some of the terms and concepts used by the poly community as I understand them. With pictures, since anytime I end up doing it in person I have to draw diagrams.
Relationship Terms
In the follow examples red (solid) lines indicate a love relationship.
Blue (dashed) lines can indicate anything from knowledge to solid friendship.
Serial Monogamy
This is the most common form of polyamory. It starts with A dating B. Then B starts looking around and finds C and start dating. Then B breaks up with A.
V's
This is the most common form of V. A and B have a love relationship. B, for whatever reason takes C as another lover. A is ok with this and can even establish some form of a relationship (either friendship or acquaintanceship) with A.
This forms of relationships can be reasonably stable, but only if B works really hard to keep everything balanced. Otherwise the V will fall over. If the relationship between A and C grows it becomes a Triad.
When the V does fall over, typically because of some problem in one of the relationship, A will have to do to a lot work to support B's relationship with C. The net result of this is that eventually it will collapse completely or return to a balanced state after much turmoil. If the V collapses completely B will typically have to decide to either keep A or C.
The other common form of V is the one where A and C have no real contact with each other. Here B must go back and forth to maintain the relationships. In this B must do even more work then in the above case. Typical, non-poly, affairs can be described in this fashion.
Triads
Triads, once established, have a tendency to be very stable. This is due, in part, to the fact that this is one of the simplest forms of polyamory. Each member is working with only two bonds, both of them love bonds and the total number of bonds that require attention is only 6.
The problem is establishing the Triad. In most cases these have a tendency to start out as a V, where the bond between the two legs grows. Many times there is turmoil as the base of the V is used to having to balance everything, and typically finds that they don't have to work as hard and slacks off when they shouldn't.
Not all Triads form from a V. Sometimes they form from two couples where one member of one couple falls in love with the other couple. So what you end up with is a Triad with a leg. This can be quite stable, but requires special attention by all of the members.
Triads break for a lot of reasons. The most common of which is that two of the individuals "gang up" on the remaining one.
W's or Chains
The W is a extended form of the V. Here two V's are joined by one of the branches of the first V. That branch, C, is then the base of the next V.
This can go on and on.
Quads
Quads are another common form of polyamory. Here four people are actually in a W with the ends closed. The quad can either be very stable, or not depending on the people involved. Each person needs to cope with 3 bonds (2 love and 1 friendship). This brings the total number of bonds to 12. Twelve bonds that constantly need attention require a lot of work.
The Quad, while seeming to be extreme polyamory is quite common. If composed of two couples (Sorry, boys in blue, girls in pink because it was easy) then a Quad is often called Swapping.
A quad that has two bisexuals is considered to be a partially integrated quad.
A quad that is completely composed of bisexuals in considered to be an integrated quad.