Rather than embrace the method employed in the other answer to the student’s question – how did Shakespeare influence the Renaissance – by inverting the question, I will attempt to answer the question as it was posed. Also, there is some questionable history in the other answer, such as the failure to understand the commonly-accepted time frame in which the Renaissance occurred, and the suggestion that religion played a less important role is misleading, as the Reformation was pretty well grounded in religious practices and beliefs, and the works of Michelangelo are replete with the artist’s fealty to the subject matter (e.g. the Sistine Chapel). The nexus of religion and politics represented by the Protestant Reformation made it a particularly important period of time, and one in which religious beliefs were reinvigorated by the rejection of the ethically questionable practices of the Catholic Church that led to Martin Luther’s actions.
William Shakespeare (1564-1616) lived concurrent with the period of European history known as the Renaissance, and it could be said that he did influence that period of time through his writings. While the Renaissance included important developments in the sciences, as Leonardo da Vinci’s contributions suggest, in religion, and in political thought, that period of time, which ran from the 14th through the 17th centuries, was defined as much as anything by the arts and literature. And, in that, Shakespeare was an important figure. His depictions of human relations were characteristic of the period in their rejection of the blatantly artificial and simplistic portraits of individuals characteristic of earlier periods, and the interactions between individuals in his plays were considerably more complex than in the occasional work of literature produced during the Middle Ages. The other answer is correct in its focus on humanism as integral to the Renaissance, and Shakespeare’s works certainly elevated the importance of a humanistic approach to literature, but this was Shakespeare’s contribution to the period, not the period’s contribution to Shakespeare.
Shakespeare’s plays are incredibly complex, interweaving narratives into multilayered stories replete with human drama and comedy – sometimes both, as in the comedic presence of the nurse in Romeo and Juliet – and there is no pretense to idealism. Macbeth is a complicated figure whose destiny could have gone any number of directions but for the pernicious influences of his wife. Shakespeare’s portrait of Shylock is the quintessential stereotype of the miserly Jew, until the playwright reminds the audience of this individual’s essential humanity through the famous protestation from Act III, Scene I, included below:
“I am a Jew. Hath not a Jew eyes? Hath not a Jew hands, organs, dimensions, senses, affections, passions? fed with the same food, hurt with the same weapons, subject to the same diseases, healed by the same means, warmed and cooled by the same winter and summer, as a Christian is? If you prick us, do we not bleed? If you tickle us, do we not laugh? If you poison us, do we not die? And if you wrong us, shall we not revenge?”
Shakespeare is celebrated for his brilliance. The Renaissance is defined as a period of time when human expression reached its full potential, and Shakespeare’s body of work was and remains one of the most important expressions of the freedom of thought that came out of that seminal period in human history. He influenced the age in which he lived at least as much as it influenced him.