The ashes in the fireplace, the ashes that fall from Angela's endless cigarettes—they're all byproducts of Angela's sad and hopeless life. Ashes are lifeless, they're what's left over when the fire goes out. So the title seems a fitting description of what the book's about: Angela's constant struggle to survive and gritty life filled with loss and disappointment.
We were about to get all deep and philosophical about how the title can also represent Frank being like the mythical phoenix who dies by fire over and over again and is reborn from the ashes each time. Then we heard Frank McCourt tell the New York Times that he'd originally intended to bring the events of the memoir up until the time of his mother's death, when he and his brothers returned to Limerick and scattered Angela's ashes. Instead, that episode became part of the sequel, titled 'Tis. Hmm. Maybe, among other things, Angela's Ashes just means Angela's ashes.