"Going to Meet the Man" is a short story published in 1965 about a police officer called Jesse, who lies in bed worrying about the Civil Rights protests that are challenging the status quo.
James Baldwin does not express explicitly who "the Man is," but most likely he means something or someone a person has to ultimately answer to. It is most likely an authority figure, such as the police or even God.
In the context of the story, he could either be talking about Jesse, who sees himself as the last of protection between the white population and the black population (particularly the ones who he sees as disrupting society), or about the person (i.e God) he will have to eventually answer to for his extreme racism. There is definitely a sense, particularly during his childhood flashbacks, that he has some empathy buried deep down toward black people and some guilt towards his own actions. For example, his inability to have sex with his wife at the beginning of the story could suggest some kind of depression resulting from his own brutality. As a religious man, this may express itself through the idea that such brutal actions are sinful and can lead to negative judgement when "going to meet the man."