The name of the company that designed the chip that powers the card.
Despite the fact that there are a ton of companies that manufacturer retail versions of video cards (i.e. BFG, Sapphire, HIS, ASUS, etc), there are only a handful of companies that produce the actual chip designs.
Retail card manufacturers take these designs from companies like nVidia, ATi, S3 or XGI and create cards which actually get put on store shelves. Along the way they add their own touches like a different circuit board color or special troubleshooting or overclocking software. In general, all these retail cards are essentially identical.
The big difference between most retail cards is the games/software that is bundled with them. Some companies bundle a large number of games with their cards to set themselves apart from other manufacturers. Other manufacturers have no bundle at all and instead market their cards as 'budget' or 'no frills'.
Some manufacturers will replace the reference card cooler with their own design, and (in rare cases) some manufacturers will deviate from the reference design to come up with something a little better. Again, all this is in an effort to set themselves apart from the two dozen other manufacturers of the same card.
Knowing the manufacturer of the chip that a card is built around is handy for several reasons. When you want updated drivers, you get them from the chip manufacturer, not the company that made your retail card. Also, you can directly compare the specifications of cards from the same company in the same generate to determine relative performance. If you compare cards from different manufacturers, subtle differences in the chips design can make the card perform better or worse than the specifications alone indicate.