At the end of Chapter 3, Mattie likens her mother, Lucille, to the captain of a ship.
Life was a battle, and Mother a tired and bitter captain. The captain I had to obey. (17)
She describes her mother this way to make a point of how Lucille is a woman who is in charge. Instead of commanding a ship, Mattie's mother commands the coffeehouse and the family. She gives orders and sets the rules for Mattie, Eliza, the coffee shop's customers, and even Grandfather to follow.
In Mattie's mind, her mother runs her affairs the way a tyrannical captain would command his ship's crew. Her mother tells everyone what to do and never accepts excuses. Lucille had lived through the deprivations of the American Revolution. It is suggested that this experience, along with the untimely death of her husband, is wat hardened her into the no-nonsense woman Mattie knows her as.
Mattie is an independent-minded girl herself. This results in a strained relationship between her and her mother. When Lucille falls ill, Mattie finds her "ship" figuratively adrift without its captain. In the end, it is the sense of perseverance and grit that Lucille has imparted on her daughter that gives Mattie the strength and courage to face the hard times that befall her when the fever descends upon Philadelphia.