These days the BIOS is stored on a flashable chip. This chip can be 'flashed' with a new version of the BIOS program to update it. Flashing is the process of loading a new version of the BIOS into the chip and then turning the voltage up on the chip momentarilly to 'burn in' or 'flash' the new program. This is all done automatically from software provided by your mainboard's manufacturer or the manufacturer of the BIOS itself.
All BIOS updates and the flash utilities should usually be downloaded from the website of your mainboard's manufacturer, as many makers customize or optimize (read: 'gratuitously tweak') the BIOS to match the configuration of their mainboard's chipsets.
IMPORTANT NOTE: YOU SHOULD ONLY FLASH YOUR BIOS IF YOU ARE EXPERIENCING PROBLEMS THAT THE MAINBOARD MANUFACTURER IS RECOMMENDING A BIOS UPDATE TO CORRECT.
If the update process to flash the BIOS to it's new version goes horribly wrong, it will turn your PC into a big paperweight, and render it totally useless. Flashing the BIOS should not be attempted by novice computer users.