What relationship is there between society and Shakespeare's work?

Shakespeare is one of the most prolific writers in known history. His plays and sonnets are internationally revered. They have also had significant impact on modern society.

There are too many ways Shakespeare has influenced our world to name here. So we'll focus on two: language and the treatment of outsiders. 

First, Shakespeare invented over 1700 words (though this number is somewhat disputed by linguists). Some of these words or phrases have grown to become mainstays in English idioms and vocabulary. Words like "amazement" (King John), "bedroom" (A Midsummer Night's Dream), and "undress" (The Taming of the Shrew) all appeared for the first time in Shakespeare's work. Phrases like "be-all and end-all" (Macbeth) or All's Well that Ends Well were brought into existence by the Bard. This is a significant contribution to the English language. 

Secondly, Shakespeare's understanding of humankind is unparalleled in his day. The famous play Othello features a black title character. In this piece, villainous characters like Iago often compare Othello (by virtue of his skin color) to an animal or use other racially derogatory language. But Othello is a masterful general and friend. During Shakespeare's life, this portrayal of a black man as heroic and commanding, not criminal and slavish, would have been a remarkable reversal of standard prejudices.

Or look at Shakespeare's treatment of the Jewish character Shylock in The Merchant of Venice. Yes, Shylock is the "bad-guy" in the play. But he's given a wonderful monologue where it becomes clear that he only does what he does because of how badly Christians have treated him. Here's some highlights from that scene:

                                            "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?... 

                                              ...The villany you

teach me, I will execute, and it shall go hard but I 

will better the instruction." (The Merchant of Venice 3.1)

Shylock makes it clear that he is simply following the example of Christians, who have treated him miserably because of his faith. 

Shakespeare saw how the majority of his time, white Christians, treated outsiders. His plays fought to reverse stereotypes and convict the audience. Our modern sensibilities have been significantly impacted by his literature.