Many computer hardware vendors use the serial number to uniquely identify a system for the purpose of maintenance requests, warranty inquiries, etc.
Typically the serial number can be found somewhere on the exterior of the case but here are a few methods for finding the number depending on operating system:
Windows
Open cmd.exe and type:
wmic bios get serialnumber
Mac
Open terminal and type:
ioreg -l | grep IOPlatformSerialNumber
Red Hat Enterprise Linux
Open terminal and type:
dmidecode -s system-serial-number