Symbolism, Imagery, Allegory
Frank McCourt basically tells us that ashes are an important symbol when he decides to include the word in the title of his memoir. Ashes come to symbolize many things here.
No Smoking, Please
Even though smoking is ruining Angela's health, it's the only pleasurable activity in her bleak life.
And [Angela and Bridey] laugh and drink their tea and smoke their Woodbines and tell one another the f** is the only comfort they have. (5.103)
And what's left after Angela smokes her cigarettes? Ashes. Residue. Garbage.
There's nothing like coming home to a warm fire after a cold long strenuous day. It's revitalizing, comforting, and warming. In fact, did you know that in many cultures, like Ancient Rome, the hearth represented the soul of homes and even civilizations? As long as the fire was burning it meant that the vital life force of the home and the city was strong (source). There was even a really important Roman goddess named Vesta, who was goddess and protector of the hearth. But, unlike Vesta, who provides for her Roman family with her warming and life-producing fire, Angela's unable to take care of her children. They're constantly hungry and cold. In other words, the fire in the McCourt household is out and all that's left behind are "dead ashes" (9.60). The ashes in Angela's Ashes are a reminder of what's missing in the McCourt household: life, warmth, food, prosperity, and health. It's why we always find Angela "star[ing] into the dead ashes in the fireplace" (13.11). Ashes are the ultimate symbol of emptiness and hopelessness.