Auguste's sapling is given during the Enlightened Journey quest by Auguste to grow into a willow tree in order to obtain Willow branches to build the basket of the balloon for the Balloon transport system. The branches can also be cut off any existing willow tree in a farming patch or obtained by trading with other players. If you somehow lose it or the tree dies, you can buy another from Auguste for 30,000 coins.
Auguste gives you the sapling for free, only the first time. With it, he gives you a basket of apples, to pay a gardener to watch over it. Growing this sapling to a willow tree takes 3 hours and 40 minutes.