Trees need leaves to get nutrients - they photosynthesize to produce energy, which travels to the branches, trunk, and roots. When it gets colder, trees shed their leaves to save water and energy for winter. The first substance to break down in leaves is chlorophyll, a green pigment, which is why leaves change color. The dead leaves contain some nutrients and organic matter, which are returned to the soil and back to the trees as the leaves decompose. This is the main reason why it is worth leaving some leaves on the ground.
Equally important for nature is the fact that the fallen leaves are the overwintering habitat of various insects, caterpillars, and pupae, which in turn provide food for overwintering birds.
Leaf piles, if left in the environment, e.g. in a corner of a yard, or by a fence, give hedgehogs a place to hibernate.