This question has been asked by many students over the years and the best way get an answer is by reading this great web-site:
THE CHEMISTRY OF AUTUMN COLORS

The answer here is directly taken from that web-site:
During summer, the leaves of trees are factories producing sugar from carbon dioxide and water by the action of light on chlorophyll. Chlorophyll causes the leaves to appear green. (The leaves of some trees, such as birches and cottonwoods, also contain carotene; these leaves appear brighter green, because carotene absorbs blue-green light.) Water and nutrients flow from the roots, through the branches, and into the leaves. The sugars produced by photosynthesis flow from the leaves to other parts of the tree, where some of the chemical energy is used for growth and some is stored. The shortening days and cool nights of autumn trigger changes in the tree. One of these changes is the growth of a corky membrane between the branch and the leaf stem. This membrane interferes with the flow of nutrients into the leaf. Because the nutrient flow is interrupted, the production of chlorophyll in the leaf declines, and the green color of the leaf fades.

If the leaf contains carotene, as do the leaves of birch and hickory, it will change from green to bright yellow as the chlorophyll disappears. In some trees, as the concentration of sugar in the leaf increases, the sugar reacts to form anthocyanins. These pigments cause the yellowing leaves to turn red. Red maples, red oaks, and sumac produce anthocyanins in abundance and display the brightest reds and purples in the autumn landscape.