The invisible man is the narrator and protagonist of the story. We never learn his name, but this is his show—the novel chronicles his path to realizing his invisibility. This is not some weird take on Heroes or X-Men, because the protagonist/narrator isn't talking about literal invisibility, but figurative/metaphorical/societal invisibility.
When people look at him, they see simply "a black man" and project various stereotypes onto him. In other words, no one sees the narrator for who he truly is. On a more positive note, being invisible allows the narrator greater freedom and mobility. While remaining under society's radar, he can cultivate his true persona.
Bonus: he can also steal things (such as electricity to supply his light bulbs).