Act 3, scene 1 is a powerful moment in the play because it includes the deaths of two prominent characters (Mercutio and Tybalt) and because it is the moment when Romeo is exiled from Verona and must, therefore, leave Juliet.
The two deaths occur in the second half of the scene, and these climactic deaths are made all the more powerful and dramatic by the contrast of the comical mood established at the beginning of the scene.
At the beginning of the scene, Mercutio taunts the Capulets using lots of sexual innuendo. For example, when Tybalt asks for "a word," Mercutio replies with, "Make it a word and a blow." Mercutio then asks Tybalt, "Could you not take some occasion without giving?" In both of these instances, Mercutio is using sexual innuendo to imply that Tybalt is homosexual. A "blow" and "giving" are thinly-veiled references to sexual acts between two men, intended to make the Montagues, and probably the audience too, laugh at Tybalt. This humor, of course, depends upon homophobic attitudes.
When the shocking deaths occur later in the scene, they are all the more powerful because of the sharp contrast with the comic mood established at the beginning of the scene.
At the end of the scene, after Romeo has killed Tybalt, the Prince proclaims, "Let Romeo hence in haste, / Else, when he's found, that hour is his last." This is a powerful, dramatic climax to the scene because Romeo's life is in danger and because he now must be separated from Juliet. This separation makes Romeo desperate and irrational, and it drives forward the rest of the plot.