Elizabeth loved the theatre. She would often have companies of actors like The Lord Chamberlain's Men perform at court. In this way she could enjoy the latest play without having to go to the theatre itself. The theatres were located in the red light district and not a proper place for the Queen of England.
It is rumored that she liked the character of Falstaff so much that she asked Shakespeare to write a play about Falstaff in love. The result was one of the two plays with no known source, a play set in a contemporary England, and Falstaff not so much in love as in lust.
A specific type of court entertainment grew out of performing for the queen, this was the court masque. In The Tempest, we see one. Ben Jonson was well know for his masques.
Under Elizabeth, not only theatre but the English language flourished. The term Elizabethan is a direct result of her love of theatre and literature.