The BIOS is basically a small chunk of firmware stored on the card which contains information about the device, configuration data for the IC, and other stuff about the card. It stands for "Basic Input Output System".
Flashing the BIOS allows you to change these setting, which can allow you to alter default clock speeds, chip ID's (which can make an OEM card "look" like a retail card) etc...
Of course, flashing a BIOS comes with some risk. Make sure you understand what your doing (and the associated risk) before you attempt to flash. A failed flashing can render a card useless.
Edit - As far as I know, flashing the BIOS will not allow a "faster" overclock. In some cases, it may be possible to adjust memory timing settings which may allow for a "higher" overclock but the net effect may not be a faster card. In general, flashing the BIOS does nothing more that most tweaker programs do.