An ash represents something that has burned up or been destroyed.  I think this represents Angela's family.  It has been destroyed.  There is no home.  Her husband is gone and her sons have died or left.  All that remains is her, and her cigarettes with the ashes falling.  The term "Angela's Ashes"  may also represent the destruction of all of her hopes.  When she met and married her husband, she had hopes of a family, a home, and a life.  All these hopes were gone now.  The only hope that she had left to her, Frank took with him when he went to America.  Her dreams, her family, they were as gone to her as the cigarettes were when she was finished smoking them; all that was left was ashes.