According to Australian understanding, a "matilda" is the pack containing the personal belongings of a "swagman," a man who seeks casual work while traveling about carrying on his back his portable shelter that is rolled up with his belongings inside. He calls this bundle a "swag". Thus in antiquated Australian Pidgin, he is "waltzing" his "matilda," or as we would say it in America, he is "carrying his backpack." As the two verses of song's lyrics indicate, he's resting under the shade of a "coolibah" (an Australian gum tree) waiting for his "billy" (a metal pot) to boil. Evidently he sees a sheep grazing nearby. He grabs the "jambuck" (sheep) and jams it in his "tucker-bag" (a container that protects his food) and takes off with it. If we were to sing the remaining verses of the song, we would find that the owner of the land arrives with the authorities to arrest him. He immediately jumps in the "billabong" (a large meandering lake) and commits suicide. As the legend goes, his ghost may be heard by those who pass that area to this very day.