“Square” often refers to someone who fits well into the system (a “grid,” if you will). The speaker in this song has decided that it is hip to be square. He used to try and fight the system, but now he has decided to fit in and be square.

The song’s inspiration was a trend in the 1980s of former hippies giving up on their cultural rebellions and joining the cultural mainstream. In a 2008 interview with Entertainment Weekly, Lewis said:

It was about a phenomenon that’s articulated much better in a book called Bobos in Paradise. The phenomenon where people from the ’60s started to drop back in, cut their hair, work out, that kind of crap, but they kept their bohemian tastes. And that’s why today, the ruling class are Bobos. They’re bourgeois bohemians. I thought it would be funnier in the first person, but I kinda mistold the joke a little bit and I think some people thought that, in fact, it was an anthem for square people.”

Famously, in the 2000 satirical horror film, American Psycho (based on the 1991 novel of the same name), main character Patrick Bateman delivers a wildly incorrect critical analysis of the song:

In ‘87, Huey released this, Fore!, their most accomplished album. I think their undisputed masterpiece is “Hip to be Square”, a song so catchy, most people probably don’t listen to the lyrics. But they should, because it’s not just about the pleasures of conformity, and the importance of trends, it’s also a personal statement about the band itself."