This encounter, which occurs in the Prologue of this novel, is important because it introduces important themes and concepts that govern the rest of the novel. Let us remember what happens: the narrator bumps into a blond white man in the dark. The blond man insults him, and the narrator tackles him, wanting an apology. He is just about to slit the blond man's throat when he realises that the blond man insulted him because he wasn't able to see him. The next day, the narrator sees the write up of this event in the newspaper but is amused to see it described as a "mugging."
The narrator believes he is an "invisible man" because he lives in a society that refuses to see him as a three-dimensional, real individual. As a result, this encounter with the blond man acts as a reinforcement of this. Because he is invisible, whites are therefore "blind" and are unable to see him, which is something that the narrator realises. It is therefore highly ironic that this incident can be refered to as a mugging, when such a term presupposes the existence of the narrator. The irony is of course that the narrator's existence is not accepted in the white-dominated society where he lives at all.