Most advanced versions of this software are —free to try for a limited period, but requiring a license to unlock full functionality. The serial number is the gateway to that full version.
If you are looking for the serial number of your physical hardware (for warranty or driver support), it is usually located on a sticker on the underside of the keyboard choosing between the free tools mentioned? Remapping laptop's keys under Windows - Libb's blog
by ATNSOFT is a paid application that requires a unique key for the full version.