Yeah, it’s a pretty old saying here in the states. It’s like saying ‘don’t be boring’ or ‘not with the party or scene or whatever is going on at the moment’. Generally the person is not ‘with it’. As in four corners man. It’s a 60’s thing.
other definitions - Square - Someone who was not “Cool”. Example: "Jerry’s so square, all he does is his homework, watch TV, and he doesn’t even like Elvis!"
Slang. A person who is regarded as dull, rigidly conventional, and out of touch with current trends.
and finally from Merriam-Webster Dictionary - Square - a person who is conventional or conservative in taste or way of life
My lesson is through for the day. There will be a test. :