Processor microcode is akin to processor firmware. The kernel is able to update the processor's firmware without the need to update it via a BIOS update.
Processors from Intel and AMD may need updates to their microcode to operate correctly. These updates fix bugs/errata that can cause anything from incorrect processing, to code and data corruption, and system lockups.
It is very difficult to know for sure whether you need a microcode update or not, but it is not safe at all to just ignore them. You might not notice their effect and have precious data silently corrupted, or an important program silently misbehave. Or you could experience one of those unexplainable and infrequent software issues (such as kernel oops, application segfaults) or hardware issues (including sudden reboots and hangs).
Releases of new microcode updates are more frequent on young processors, but the release of new microcode updates for older processors do happen.
The BIOS (or EFI) updates the CPU microcode during boot, however most of the time either the motherboard vendor won't issue frequent BIOS/EFI updates, or the user won't install such updates. For these reasons, the system processor is likely to be running with outdated microcode on a vast number of systems.
Updating CPU microcode within Debian (Intel or AMD)
Please install the amd64-microcode package (for systems with AMD AMD64 processors), or the intel-microcode package (for systems with Intel processors). You will have to enable both contrib and non-free in /etc/apt/sources.list.
Debian 6.0 "Squeeze" users can find up-to-date versions of these packages in the official backports repository (in the contrib and non-free sections).
Microcode updates will be applied immediately when the microcode packages are installed or updated: you don't have to reboot. You will have to keep the packages installed, though: as explained above, the microcode updates have to be reapplied at every boot.
Checking the microcode version of your CPU
You can check which version of the microcode your processors are running by looking for "microcode" lines on /proc/cpuinfo. This information is only available on recent kernels (such as the Debian 7 "Wheezy" kernel).
ANNOUNCEMENT: Intel/AMD x86 CPU microcode update system in non-free at debian-devel mailing list.