The "monkey" in the Monkey Trial refers to the metaphorical notion of humans being descended from apes. This association arose from Scopes' teaching of Charles Darwin's theory of evolution, which suggests that humans and apes share a common ancestor.
To summarize, the Monkey Trial was a court case that focused on the teaching of evolution in schools, sparked by the prosecution of John Scopes for violating the Butler Act, and is metaphorically associated with the idea of human evolution.