Assuming this question is referring to European medieval drama, the most important point of all would be that theater was highly religious in nature. The Roman Catholic Church was a major player in everyday life and so had a great deal of influence over theater during this period.
Plays often dramatized Biblical stories such as Noah's Ark or the birth of Christ. Since laypeople were forbidden to read the Bible and most were illiterate anyway, the theater was a great way to teach people these stories while also entertaining them. Though these stories were considered sacred, the performers would add a little humor as well, appealing to the lower classes' comedic sensibilities as they educated them. For example, a dramatization of Noah's Ark made light of Noah's marriage, interpreting his wife as a shrew and Noah himself as a henpecked husband.
The Second Shepherds' Play is a famous example of medieval drama. It takes place during the birth of Christ but first focuses on humble shepherds who find their sheep has been stolen by a comically wicked couple. After that part of the play is resolved, the story ends with the shepherds visiting the Christ child and the Virgin Mary at the manger. The tone is quite humorous throughout despite the religious matter. The writer knew to balance both religious sentiment and comedy, keeping both the Church and the audience content.