The Renaissance was a dynamic era that looked back toward the past with delight, relished the present, and struck out toward the future. It valued the human person, the glories of classical Greece and Rome, and the expansion of the known world through exploration and discovery. These values are reflected in the drama of the Elizabethan and Jacobean periods.
Let's look at some examples of how this worked. In the medieval period, drama was largely centered around the Bible. Mystery plays and morality plays dominated the scene as actors presented Bible stories and moral lessons for eager audiences.
In the Renaissance, however, the subject matter of drama greatly expanded. Think, for instance, of the broad scope of Shakespeare's plays. They cover everything from ancient Rome (Julius Caesar, for instance) to Denmark (Hamlet) to England's history (Richard II, Henry IV). Quite a few are set in the era of classical Greece, showing the Renaissance appreciation for that time but also the Renaissance innovation that made Greek ideas and characters relevant for the Renaissance era.
Renaissance drama also tended to focus on the individual. Examples here include Christopher Marlowe's Doctor Faustus and Shakespeare's Macbeth. Renaissance dramatists created characters that are complex and nuanced. They are not allegories or types, but real individuals with real issues, challenges, and choices.