Why leaves change color is somewhat of a complex idea but I was able to get a little help from Dr. Brenda Lackey from UWSP.
One of the most important concepts is that the changing of leaves' colors all begins in fall when we start to lose sunlight. Ironically enough, it is the fact that the nights are getting longer that the plants notice. Because of this, the plants begin to prepare for less sunlight and cooler nights by draining their nutrients into the tree's branches, and trunks for storage in the winter, their dormant time. This process actually causes leaves to stop producing chlorophyll which is sensitive to the cold. Remember chlorophyll is the ingredient the plant uses during the summer months to convert sunlight into food. Chlorophyll is also what gives the leaves the green color you see through the summer.
Since the chlorophyll is no longer dominant, the other pigments that have been in the leaves but have been covered begin to surface and show. There are two main other types of pigments: the carotenoids which show up as yellow and oranges and the anthocyanins which are the reds and purples. The carotenoids almost always remain constant from year to year but the intensity of the anthocyanins is very dependent on the weather. The anthocyanins actually help allow the plant to recover nutrients in the leaves before they fall off the tree. This helps for the next growing season.
To determine what kind of fall color season we will have, you need to go back all the way to spring. For a very nice showing of the reds we need to have seen a warm wet spring, a summer that is not overly hot or dry and an autumn with sunny warm days and cool nights. Cloudy and overcast days along with nights of frost or freezing will affect the amount of color and could possibly kill the leaves.
In recap, plants have three types of pigments. In the summer the chlorophyll is dominant therefore the leaves look green. During the fall, when they stop producing chlorophyll, we can finally see the secondary pigments, carotenoid (which has always been in the leaf). The cartoenoids are constant from year to year but the final pigment, the anthocyanins produced in the fall, are dependent on the weather we have seen all year long.
For more information on what tree produces what colors check out the "Different Trees, Different Colors" video.