One of the reasons that this play has such a dramatic opening is that it completely plunges us as an audience into the thick of the action, as we see the reality of the Montague/Capulet feud in all of its gory realism, and at the same time are introduced to two characters who are inextricably intertwined with it. It is interesting to note, however, how this fight between Benvolio and Tybalt actually forshadows the confrontation later on with Romeo and Tybalt in Act III scene 1. Note how in Act I scene 1 Benvolio tries to play the role of peacemaker, but is forced into conflict against his wishes, just as Romeo tries to avoid violence in Act III scene 1. Note what Benvolio says to Tybalt as he pleads for peace:
I do but keep the peace. Put up thy sword,
Or manage it to part these men with me.
In spite of his best intentions, Benvolio finds himself sucked into violence against Tybalt, because of the way that Tybalt's character is so opposed to peace, just as Romeo, against his desires and wishes, fights Tybalt later on in the play.
Thus the importance of this fight lies in the way it foreshadows the later confrontation of Romeo and Tybalt, and also in how it focuses on the way that, in spite of our better judgement and our attempt to avoid violence, we can nonetheless find ourselves sucked into it, just as Benvolio was forced to fight Tybalt.