I like the creative names on SE badges, but a couple of them went over my head. What is "mortarboard"?
A mortarboard is the name of the cap worn by someone graduating (e.g., from high school or college).
From thefreedictionary (definition 2), a mortarboard is:
An academic cap topped by a flat square.
Presumably it was chosen for the particular badge of, "Earned at least 200 reputation in a single day" to symbolize a degree of academic merit.