Its the new "catch phrase" everyone is saying. By saying your so square, your basically saying your so bad ass, or cool. Basically if your square, your awesome. If not, then you must be a nasty triangle.
1) A 4 sided shape where all 4 sides make right angles
2) A type of person who doesn't like to see people have a good time. The word has old origins, there is a connection between the shape of a Europeans face and the use of the word.
A group of Indians see a group of square faced white men approaching their fire. One points and smiles and says square what do you want?
The Europeans tell them- You Indians having a good time over here? Not any more, if you stay your children will be slain and your women will be raped, what's left of you will pack up and move to Oklahoma or wherever we decide to send you. Now, you, the strong looking one, come with us.