A metaphor is a figure of speech that directly refers to one thing while mentioning another one. Metaphors are meant to establish clarity between ideas, or a link that connects them.
In this case, Martin Luther King Jr. presents the metaphor of "cashing a check" in order to refer to the Civil Rights Movement. His argument is that the United States had given black people a "check," which refers to their rights. However, these had not been realized. Therefore, in "cashing" this check, black people were asking to receive what the country had promised them before: equal rights.
