Severity means seriouness of a defect.
Severity levels are critical, major, minor.

Critical : Its going to abort the application.I.e when user 
clicks on Register link in  a home page,then Run time error 
page is displayed.

Major : Funtionality of an application is not working.
I.e when user fills the registeration form. If that details 
doesn't entered into the Database

Minor: User interface releated issues.like look and 
feel,Typo's and Grammar's issues.

Based on this severity level, Tester can assign serverity 
for a defect

Severity always can be considered w.r.t functionality 
i.e "seriousness of defect w.r.t functinality " is severity