There are 3 main symbols that represent polyamory.  One is the parrot (as in "polly wanna cracker?").  Some don't like that symbol because of the Jimmy Buffet reference - especially those of us who live here in Florida.  The upside to the parrot is that, here in Florida, there are certainly lots of parrots to be found!  Another is the Heart / Infinity symbol.  Some don't like that symbol either because they're not fond of hearts (some think it's too "feminine").  The third is a flag with blue, black and red, and a pi symbol in the middle.  This never really caught on because no one knows or remembers what the pi is suposed to stand for (the greek letter for "pi" translates to just "p" in English and is supposed to be the "p" in "polyamory" in this case).
In a forum there was some discussion about coming up with a better/alternative symbol.  Something other than the silly parrot pun, something less feminine than a heart, and something more memorable than a pi symbol.  The Purple Triangle Mobius was born - not to replace all the other symbols (we're poly, after all, we embrace the power of AND!), but to complement and to be an alternative symbol that fulfilled a niche that the others didn't.
A Mobius strip is a never-ending strip.  The infinity symbol (from the Heart / Infinity image) is one example of a Mobius Strip.  The easiest way to understand a Mobius Strip is to imagine a long strip of paper.  Now imagine twisting it once.  Put the two ends together to form a loop and that's a Mobius Strip.  If you were to draw a line lengthwise down the middle of the strip, starting at the point where the two ends meet, you would start on the outside of the loop.  The line would then move to the inside at the twist, and come back to the joint but on the backside from where it started.  You could continue to draw the line, twisting back towards the outside at the twist, to eventually end up where you started in a complete unbroken line that is twice as long as the space it takes.  As long as there is an odd number of twists, this is what will happen when you try to draw that line.
A Mobius Strip was used to reference the more traditional infinity symbol (which stands for "infinite love""), but instead of the normal figure-8 design, it was turned into a triangle shape.  This makes reference to several other groups that the poly community has connections to: the gay community with its pink triangle, the lesbian/feminist community with the black triangle, the bi community with its 3-looped symbol and the double triangles, and even (very distantly) references the Top/bottom/switch Triskelion with its 3 pointed design.  The purple color was chosen because purple seems to be a common color choice in many poly designs, as well as a featured color in the gay pride movement and the bisexual symbols.  The direction of the points also references the heart symbol of the traditional Heart / Infinity as well as the direction of the various triangles of the other alternative sexuality movements. 
All the references together are supposed to add up to symbolize "infinite love" and "alternative sexuality" by nodding towards all those groups and subcultures and symbols that came before it.

This design was created by Joreth of The InnBetween (www.theinnbetween.net) in May of 2009 and is intended to be public domain.
File:Mobius-purple.jpg
Original: Joreth InnkeeperVector: Mnmazur