Interludes, mystery plays, and morality plays are three medieval dramatic forms that preceded Shakespearean drama. However, each of these forms influenced Shakespeare in myriad ways.
Interludes were short, often farcical dramas that were performed between the sections of a longer play or in a sequence of entertainment. Within several Shakespeare plays, the characters watch interludes that are performed within the context of the play. For example, this happens in A Midsummer Night’s Dream with Pyramus and Thisbe after Theseus and Hippolyta’s wedding. In this example, the comical nature of the performance mirrors the qualities of an interlude.
Also known as miracle plays in literary parlance, mystery plays were typically about religious subjects. While none of Shakespeare’s works are strictly Biblical stories, they do feature some of the hallmarks of mysteries. For instance, both Shakespearean and mystery plays featured minimal set design that changed very little from one production to the next. Both also included satirical elements that mocked stereotypes using what are called "stock characters," such as the fool that frequently pops up in Shakespeare’s plays.
Turning to morality plays, Shakespeare borrowed the concept of the moral value characters. These characters are symbolic stand-ins for a particular concept, like greed. For instance, Richard III is widely regarded in Shakespearean scholarship as a medieval “Vice” figure, who represented pure evil or Satan. Vice was a common character in morality plays.
These are just some examples of how Shakespeare and these earlier dramatic forms are similar.
One common element could be the use of dramatic suspense, when the audience knows something that the characters do not. Shakespeare used this frequently to build suspense, like in Hamlet, when the audience knows that Polonius is hiding behind the curtain, eavesdropping on the Queen and Hamlet's conversation.