The master of the vineyard, which we presume was our Heavenly Father, said he would prune his vineyard, which seems to mean that he would cut out the dead wood, and then he would dig around it, which probably meant that he would stir up the Israelites and thereby provoke them to good works. Finally he said he would nourish this precious tree, and we learn from Jacob 6:7 that the "nourishment" of heaven is "the good word of God," or the scriptures, and we therefore assume that this present passage has reference to the giving of additional revelation specifically designed for the spiritual nourishment of Israel.
Out of all of this effort the Master hoped his dying tree would produce some young and tender branches. The olive tree has the rather unique capacity of being able to grow new trees from "young and tender branches" which are cut off from the parent plant and transplanted elsewhere.