So you want to know why the leaves change color. Before I could tell you how and why leaves change color, you must first know a few principles of light. Visible light is actually made up of electromagnetic waves of different lengths. These are the same type of electromagnetic waves as the waves that carry the voice of your cell phones. However, the frequency of the waves of visible light is much higher. The relationship between the frequency and length of a wave is inversely proportional. Therefore, higher the frequency, the smaller its length is. Visible light is measured in nanometers. In general the human eye is able to see wavelengths between 380-780 nm.
Each color has a defined wavelength. For example, red can be found in the region between 620-680 nm. We must not forget that the color spectrum is continuous. There is no border between two colors. So there are an infinite number of colors.
Well enough about waves. For simplicity, nature gives us one of the best show out there and that can help us understand, the rainbow. Isaac Newton separate the rainbow in seven colors: red, orange, yellow, green, blue, indigo and violet. This is simple, the humain eye can see the seven colors of the rainbow and the white light is the sum of all these colors.