In Romeo and Juliet, the feud between the Montagues and the Capulets will only be resolved after Romeo and Juliet's love for each other result in their deaths.
Romeo, not yet having laid eyes on Juliet and besotted with Rosaline (who refuses to return his love), plans to attend the Capulet ball uninvited because he knows that Rosaline will be there. He is discussing his situation with his friend Mercutio in Act I, scene iv as they are on their way to the Capulet's ball. Romeo thinks love is very hard and his "soul of lead" (15) indicates how stressed he is; he is convinced that "Under love's heavy burden do I sink" (22). Mercutio recognizes Romeo's feelings for Rosaline as not indicative of real love. It is in his nature to mock love as he finds a far more practical use for it and suggests that Romeo should do the same. Much of what he says has connotations of a sexual nature. Lovelorn Romeo does not think he is in the mood for the festivities that will follow shortly at the ball.
As they are attending a ball, they are carrying masks, a tradition of the time. Mercutio says, "A visor for a visor!" (30). Mercutio is pointing out that in real life, he already effectively wears a mask, not revealing his true self. He is now swapping this "visor" or mask for another—the real mask he will wear to the ball. Both conceal the person behind them.
*All quotes are taken from The Norton Shakespeare, based on the Oxford Edition.
Mercutio's quote reads: "Give me a case to put my visage in,/A visor for a visor."
Interpretation: "Give me a mask to put my face in,/A mask to cover my mask." Mercutio is referring to his own appearance, which he believes is ugly and unattractive. Mercutio wants an attractive mask to hide his ugliness.
On one level, Mercutio is saying he is putting his mask away because he doesn't care who sees his face, injecting some self-deprecating humor. However, for Shakespearean audiences, this was also a little nod to the Groundlings. A "case" is slang for female anatomy, and "visage" is another word for face. His mask, thus, is no more than a visor for a vicer. Have fun with that one, freshmen. How many other pieces of evidence can you use to argue that Shakespeare was a dirty, dirty man?