The time period of the setting of Romeo and Juliet is important to the reader in understanding the relationships among the aristocratic families in Verona, Italy, male and female roles, interpersonal relationships within families, the role of the Church, marriage customs, celebrations, friendships, and feuds.
In fourteenth century Italy, young males were allowed to move freely about, but the females were quite sheltered. With such freedom, when tempers flared, swords were often pulled, especially with the enmity between the two feuding families of the Capulets and the Montagues. Entire households were loyal to the family, too. Of course, the feud between the Capulets and the Montagues underpins the entire action of this drama.
In aristocratic families, the daughters, like Juliet, led sheltered lives and had their marriages arranged for them at young ages. Thus, such an action as Juliet's secretly marrying Romeo, and his being an enemy would be outrageous. This is why Juliet exclaims upon learning of Romeo:
My only love sprung from my only hate!
Too early seen unknown and know too late!
Prodigious birth of love it is to me
That I must love a loathed enemy. (1.5)
An understanding of other characters such as the Nurse, who is a poor relative who lives with the family and tends to the children; the Prince as ruler who can dictate what must be obeyed, the respected position of the Church and priests (Juliet says she must confess to Friar Laurence in Act IV as it is the only way she can leave the house without an escort) is important to know, also, as these conditions make real the feelings and actions of the characters. For instance, there really is no reasonable way that Juliet can explain her marriage to Romeo to her parents without his being killed and she being sent to a nunnery.
That the family feud, which fuels the action, has been in existence for generations can only happen in earlier times such as the fourteenth century because then people stayed in the areas where they were born. Five family members of the Capulets and Montagues die before peace is finally made. So, this time period is crucial in lending verisimilitude to so many of the actions of the play.