Prince Escalus is vital to the story because he represents the voice of law. He is also vital because, as the voice of law, he speaks the lines that most clearly portray the moral that is found in the story, namely, that violent, passionate feelings lead to dismal destruction.
Prince Escalus represents the character who is most dedicated to creating a peaceful Verona and does so by laying down the law to ensure that peace is kept. In the very first scene, we especially see his desires for neighborly peace in his use of diction in the speech he uses to put an end to the third whole-city riot the Capulets and Montagues have started. The use of the word "peace" in the phrase "enemies to peace" certainly points to his desires to create peace in Verona. Also, in the line that he uses to address Lords Capulet and Montague, "Profaners of this neighbour-stained steel-- / Will they not hear?," the use of the word "neighbours" also shows his desire to create peace among the neighbors of Verona, which is how it should be. The phrase "neighbor-stained steel" refers to their swords that are stained with each other's blood. The image serves to capture the outrage Prince Escalus feels towards the ridiculous feud and his determination to put an end to it and create peace.
Besides being the initiator of creating peace, we especially see Prince Escalus relay the moral of the story in the final scene when we see him lay the blame on Lords Capulet and Montague for many deaths, including the Prince's own kinsman, Mercutio, and Romeo and Juliet. Prince Escalus clearly describes the destruction that uncontrolled, violent, passionate emotions create in the lines:
Where be these enemies? Capulet, Montage[Montague],
See what a scourge is laid upon your hate,
That heaven finds means to kill your joys with love! (V.iii.302-304)
In using the word "scourge" Prince Escalus is making the point that Capulet and Montague have been punished by God for their ongoing hatred, thereby showing us the moral that uncontrolled, violent emotions bring ill-fate.