It is derived from the French name for the madder plant (this was posted somewhere on the board when the color first came out--I think one issue of Le Monde referred to Rouge Garance as Madder Red) --see below:
From wikipedia: http://en.wikipedia.org/wiki/Madder
It (Madder) has been used since ancient times as a vegetable red dye for leather, wool, cotton and silk. For dye production, the roots are harvested in the first year. The outer brown layer gives the common variety of the dye, the lower yellow layer the refined variety. The dye is fixed to the cloth with help of a mordant, most commonly alum. Madder can be fermented for dyeing as well (Fleurs de garance). In France, the remains were used to produce a spirit as well.
It is one of my favorite reds--very wearable, striking without being glaring. It is a touch warmer than blue-red (esp. in Togo and Epsom) in my opinion, but I would definitely not classify it as being orangey-red like Vermillion (which is actually more tomato red IMO). It is richest and brightest IMO in Clemence--which is the leather shown in the auction photo (although that picture looks more orangey on my screen that it is IRL).
In addition to the aforementioned leathers it is available in Chamonix and Vache Liegee. If you are looking for a red with more of a pink/cooler undertone, Rouge VIF in Fjord is very beautiful--although not too far off in color than Rouge Garance in this particular skin. Rouge VIF in Chevre (not being produced right now) is shown in my avatar in a smaller accessory--although it is actually more blue-red than the photograph suggests.
There is an old thread called "Madder red?" which you might find interesting....Rouge Garance had just been introduced, and in the english version of Le Monde, it was called Madder Red.....
I have a Rouge Garance Clemence Birkin which I absolutely adore! I'm a "neutral girl" so bright coloured bags ARE NOT for me, but I find this shade of red just perfect: it's a true RED, with no pink undertones like Rouge Vif (too "girly", for me) and no orange undertones like Vermillion (too bright). I don't have any pics, but I'll try and take some soon!