In "Battle Royal", the narrator has been completely humiliated doing what he was taught to do--giving the whites their "yessuhs" and always being complacent and accomodating to the whites who are in charge. After the battle, the narrator gives the speech for which he came to the arena for in the first place. He can barely catch his breath, and the audience is being rude and half-listening at best.
When he dreams of the grandfather and he his him say "Keep this nigger boy running" and then laughs, it appears that the grandfather is sending a message to be aware of what he should do in life- not what he has been told and not the way the grandfather had lived. It always implies that the narrator should keep his eyes open for things that change and seize opportunities presented.
“Battle Royal,” 1947, was Ellison's first chapter of Invisible Man, which is introduced by the first-person narrator’s explanation of how as a black, he is considered so unimportant by white society that he is virtually non-existent (invisible).
A major strand of the speaker’s consciousness is his grandfather’s advice to consider kindness and submission as a subversive activity (paragraph 3). We may construe the narrator’s dream (paragraph 106) as a description of his circumstances in the face of racial discrimination. In the dream, empty envelope after empty envelope indicates the hollowness of white promises for black improvement, and the final words, “Keep This Nigger-Boy Running,” vitiate the sincerity of whites (paragraph 107.)
He has been asked to give the same speech before a meeting of town dignitaries, and goes to the meeting expecting to be received warmly and sympathetically. Instead of such friendliness, he is shown the very worst and most discriminatory vindictiveness of the members of the town’s white power structure.