Cantabridgian can mean either:
A resident student or researcher at the University of Cambridge UK.
A native (IE born in or moved to while in infancy) Cambridge resident. As Londoner is the collective noun for London residents, Cantabridgian applies for Cambridge (UK).
I am Cantabridgian, I was born in Cambridge.
Someone who lives in Cambridge Massachusetts. As a rule, someone who is far less cool and culturally relevant then they think they are.
Person 1: I love Boston!
Person 2: Have you ever been there?
Person 1: No, but everything remotely intelligent and hip about Boston is actually in Cambridge.
Person 2: Oh right, your a Cantabridgian.
One who attends University of Cambridge
Occasionally shortened to "Cantab." Obviously, this abbreviation is very easy to joke about.
Considering the fact that they attend the aforementioned university, this person is pretty much going to be a genius.
Mum, when I grow up I'm gonna be a smart Cantabridgian and I'll go learn at a big smart university and it'll be great cause I'm gonna have so much fun punting on the River Cam and everything, I can't wait to grow up!