At the beginning of the novel, Martha outlines her earliest memory, which centers around a jigsaw puzzle of the English counties. She remembers that there would always be one piece missing and that her father would always appear at this moment and, playfully, "find the missing piece in the unlikeliest place."
Her father later leaves and doesn't return until later in her life, when she has grown up. He therefore, metaphorically, takes this piece of the jigsaw with him. Because he would so often appear with the final, missing piece, Martha subsequently associates his absence with that missing jigsaw piece. Or, to put it another way, her father, through this memory, has become synonymous with the missing piece of the jigsaw. Metaphorically, this jigsaw comes to represent Martha's life, which, to her mind, has a piece missing. And to extend the metaphor further, what is missing in Martha's life as an adult is perhaps what she would have otherwise gained, and nurtured, from the affections of the father-daughter relationship that she lost as a child. Martha now, as an adult, subconsciously longs for her father to return so that he can fill the hole she imagines exists in her life as an adult.