The accordion starts off as a symbol of hope and comfort. When Liesel begins reading to the residents of Himmel Street during the air raids, she feels like she's giving them what Hans gives her when he plays the accordion – distraction, comfort, and hope.
For Hans, the accordion is a symbol of the man who gave it to him, the man who saved his life. That man is Erik Vandenburg, Max's father. For Max, the accordion symbolizes the possibility that he'll survive the Holocaust. It's the link between him and Hans Hubermann, the man willing to risk his life to help him.
When Hans leaves for Essen, he leaves the accordion behind. For Rosa in particular it becomes a symbol of Hans himself. When Liesel sees her wearing it ever night, but never daring a note, she realizes how much Hans means to her foster mother.
When Liesel finds the accordion among the wreckage of Himmel Street after Hans has died, it is a symbol of great loss, but one which carries much of her story within it. It is yet another symbol of the novel's argument that literature, music, and other arts can provide sustenance in times of great suffering.