How is theatre historically relevant to society?
There are two ways in which your question can be interpreted.
1. How is theater used as evidence by historians? The answer is that, Aristotle states, theater portrays unactualized probables, and thus tells us about the common beliefs and ideas and customs of specific periods. While the actual events of "The Peace" or "As You Like it" did not happen, they both reveal attitudes towards such things as war, politics, and sexuality in their respective periods.
2. How does theater interact with social and political movements? For this reading of your question, the answer would be that it holds up models for people to imitate or avoid. Comedy makes fun of things of which society disapproves, teaching viewers limits of acceptable behaviour and tragedy often offers models for emulation.