The kids ate the food that their mother brought home from her job at Chase Manhattan Bank.
The author's mother, Ruth, works as a typist at Chase Manhattan Bank; she works on a swing shift, which means that she isn't home until 2 in the morning. The cafeteria at the bank serves free food for employees, and Ruth takes food home from the cafeteria to bring to her children.
James McBride says that the kids all made an effort to be the first one to grab her purse. She brought home things like bologna sandwiches, cheese, cakes, and other items. If they were the first one to get to it, they ate well. If they weren't, they might not eat at all.
McBride says that the food from the cafeteria was better than the food that Ruth cooked. He says that her grits were like sand and butter and her pancakes had eggshells in them—his little brother called her stew prison stew.