A square consists of four couples, with one couple stationed on each of the four sides of the square. Everyone starts facing the center of the square. Each couple consists of a "boy"/"man" and a "girl"/"lady", with the boy standing on the left.
The actual sex of the dancer is unimportant as long as everyone remembers who is the "boy" and who is the "girl".
The lady on a man's left is his corner, and conversely the man on a lady's right is her corner. The end of dansing we must need to find the first corner.
Square dances begin in the square formation. As the dance progresses, new formations occur, and you might find yourself at some points in the dance with a partner who is not your original partner.
At any particular point in time, your partner is the person standing alongside you, and your corner is the person across the corner as described above. For example, a call to "swing your partner" would mean to swing your current partner, NOT your original partner from the starting square if that is different from your current partner.
However, your designation as man, lady, head, side, or couple 1, 2, 3, or 4 will remain with you throughout the entire dance from your position in the starting square.
That is like a game.