"Flashing a graphics card" is just a short-hand way of describing the process of writing an image file (BIOS, UEFI, EFI, Open Firmware, etc.) to the card's own "Flash" memory. Typically something like nVFlash is used to do the deed. The image file holds all kinds of information from ID strings to voltage and timing tables - besides a lot of other stuff too. These image files can be downloaded from the card's flash memory, modified, and written back in order to get the card to behave differently. The image files can also be completely replaced with a different type.
Typically this is illegal as in order to get the "other type" someone had to steal it! That's theft if you don't happen to own and retain ownership of both cards. To then turn around and sell this stolen property is HIGHLY unethical and prosecutable! Normally such "flashing" or "hacking" is offered for free as a step tutorial where the end user is responsible for obtaining the files in question - hopefully through legal means but often a blind eye is turned at this point because it's an individual typically undertaking a not-for-profit process. You can think this is basically the difference between downloading an MP3 file (from a CD you own or illegally from the internet) for your own use and burning that file to a for-sale CD and selling it. Massive difference!
I'm more than a little shocked that there's a user here doing just that (selling stolen property) and MacRumors even supplies him with a "Vendor" tag.
Anyway, that's basically what flashing is.
