A computer's Basic Input Output System and Complementary Metal-Oxide Semiconductor together handle a rudimentary and essential process: they set up the computer and boot the operating system.
What is the BIOS update?
As with any software, your computer or motherboard manufacturer periodically updates the BIOS to fix bugs, add compatibility with new devices such as new CPU models, improve caching functions, and make several other hardware tweaks that can speed up your boot time and fix annoying issues.
As far as the pcpartspicker warning goes, that is a fairly old warning. It may no longer be the case that you need a BIOS update for new CPUs.