It means he's hopeful that someday he'll be able to sit with white people and be seen as equal, not less than.
Explanation:
One line that leads up to when he says, "I'll sit at the table when company comes," is, "they send me to eat in the kitchen when company comes." Here, he's talking about how the (white) guy he works for sends him and his black "brothers", as he refers to them as, to hide in the kitchen when they have company because of their skin colour.
