I read this on The Oatmeal:
Hey, he is clapping along to the music! How
quaint! I should too. I would not want
to look like a square!
Another one:
You Won't Look Like a Square With
B-Side's Cubic, Steam-Punk Jewelry
(Emphasis added.) Now, what does it mean by looking like a square? Amazingly, Google doesn't know what that means.
Best Answer
A Google search for define:square gives me as one meaning
which is what "square" means in your example.