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There are several reasons why the Moon appears to have different colors.  The most common reason is its position in the sky.  Ordinary light is made up of a collection of waves of different lengths.  Each length corresponds to a different color.  Red light has a wavelength of 680 nanometers (there are 1,000,000 nanometers in a millimeter).  Violet light has a wavelength of 410 nanometers, and the other colors have wavelengths between 410 and 680 nanometers.  The Moon reflects the light from the Sun and all the colors are mixed together.  When this happens the light (and the Moon) appears white.  But the different wavelengths don't pass through our atmosphere equally.  It is harder for the blue and violet light to pass through.  When the Moon is high in the sky, the light doesn't need to pass through so much atmosphere and most of the light gets through and the Moon appears white.  But when the Moon is near the horizon, the light has to pass through a thicker layer of atmosphere, and some of the blue and violet light is lost.  As a result the Moon appears more red.  The same thing is true for the Sun.  When it is high in the sky it appears yellow-white, but near sunrise or sunset it appears redder.