A square being a nerd, geek, dork...un-hip, un-cool, unpopular, not with-it, etc. ...sort of person..."be there or be square" means about the same as "everyone who is anyone will be there", which is to say if you're not there you're nobody.
All the hot girls and all the rough boys will be at this party/club/place dude be there or be square!
square [skwɛə] квадратный