This first sentence is an example of hyperbole (an exaggerated statement) because it is impossible to carry around a bag so large that it contains all of your personal possessions. However, by using hyperbole in this manner, the author makes an important point about Mrs. Jones. Specifically, he indicates that she is a prepared and experienced woman. She is ready for any eventuality, and, no matter what trials and tribulations she encounters, she knows exactly how to handle them.
By characterizing Mrs. Jones in this way, the reader knows that she will not react in the expected way when the young boy tries to snatch her purse. She is not going to simply hand it over to him. This also foreshadows her kind reaction to Roger, in which she takes him to her home, feeds him, and gives him some money.