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Square used as slang may mean many things when referring to a person or in common language.
In referring to a person, the word originally meant someone who was honest, traditional and loyal. An agreement that is equitable on all sides is a "square deal". During the rise of jazz music, the term transformed from a compliment to an insult.
Negative connotations 
In the parlance of jazz, a square was a person who failed to appreciate the medium, more broadly someone who was out of date or out of touch, hence the saying "be there or be square". In the counterculture movements that started in the 1940s and took momentum in the 1960s a "square" referred to someone who clung to repressive, traditional, stereotypical, one-sided, or "in the box" ways of thinking. The term was used by hipsters in the 1940s, beatniks in the 1950s, hippies in the 1960s, yippies in the 1970s, and other individuals who took part in the movements which emerged to contest the more conservative national, political, religious, philosophical, musical, and social trends. It comes from the square representing a four-beat rhythm as shown by a conductor's hands. It was in this context that Sly and the Family Stone's trumpet player Cynthia Robinson yelled out in the hit "Dance to the Music": "All the squares go home!" If the counterculture was a shift from conservatism to liberalism, then square was what liberal people called conservative people and things. While the term waned in popularity by the 1980s, it remained in the public consciousness, particularly of the American baby boom generation, enough that its broad meaning (of a person who respects traditional principles) is exemplified in Huey Lewis's 1986 hit Hip To Be Square.
- The warden said hey buddy don't you be no square
- If you can't find a partner use a wooden chair
One of the earliest records with the usage of the term can be found in the 1946 recording by Harry Gibson "What's his Story?," which includes the stanza:
- At the gate stands a sinning fool
- Shouting "Lordy Lordy"
- Saint Peter said "You square,
- Your place is way down there"
- And the square said, "What's his story?"
Or an earlier song by the same artist, from 1944, called "Stop That Dancing Up There," which includes:
- The people downstairs
- Say I'm an awful square
- When I shout, "Stop that dancing up there."
Moreover, in Quentin Tarantino's film Pulp Fiction, Mrs. Mia Wallace calls Vincent Vega a 'square' for not going along in her plans. She draws a box in the air with her finger, which becomes visible to the viewer as a square.
Positive connotations 
Square can mean good and honest, a sense preserved in the phrases "fair and square", "a square deal"; or upstanding, as in "squaring up" (to an antagonist). As a symbol of rectitude, the square, or set-square, is one of the principal allegorical symbols in Freemasonry.
The chorus of the George M. Cohan song "Mary's a Grand Old Name" concludes with these lines:
- And there is something there / That sounds so square / It's a grand old name.
L7 is also a derivative term for square. This derives from a gesture in which the square shape is made by putting together an "L" made with the left thumb and index finger and a "7" made with the right thumb and index finger.
- Let’s not be L7, come and learn to dance.
- It will be L7 and I'd never get to heaven
If I filled my head with glue
The Sandlot's Squints used this line to describe Smalls:
- Come on, Benny. Man. The kid is a... L7 weenie!
Obie Trice in Adrenaline Rush:
- "You L7 like a square be" (sic)
XV's song "Be There, Be Square" referred to L7.