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It is constant, because it's determined by the electrical properties of the
vacuum or material stuff it's traveling through. So as long as the electrical
permittivity and magnetic permeability of the medium don't change, the
speed that they determine doesn't either.
The constant speed of light "C" (for example in E=mC2) is the speed of light in a vacuum. Light in other mediums, such as glass, moves slower and creates such effects as refraction.
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