Because wine speaks of life, vitality, transformation, it is often a symbol of the Holy Spirit in Scripture. Wineskins, of course, are made of leather, and new leather is very pliable.
Old leather is rigid and cracks easily.
Jesus was saying that the kingdom is always in fermentation. In grape juice or other organic material, fermentation is a chemical reaction that causes expansion, which is why the cork on a wine bottle pops when first opened. Jesus was teaching here that people who want the new wine of the kingdom of God must be flexible. Kingdom life is too dynamic to be contained by rigid skins that it cannot shape. God's kingdom will not settle into the shape of any earthly mold.