This is a great question, and very difficult to answer.
Sound waves require a medium to travel through. That is, a mass of molecules. The speed of sound depends on the density of these molecules, which is why there is a different speed in water and air, and why there is no sound in the vacuum of space. Also, you notice how sound dissipates, which is the sound wave 'giving up' energy to the molecules it travels through.
Light on the other hand does not require any medium. It just keeps going through space at a constant speed untill it is absorbed. All of this lies in the theory of electromagnetism (light is an electromagnetic wave).
It is these properties (sound waves require a medium to travel in but light waves do not) and the fact that light waves are electromagnetic in nature that dictates their different speeds.
But to answer why they are different, opposed to how they are different, needs someone with a little more knowledge of electromagnetism than me! Steven Hawkins, a little help please...
Evans is right that this is a great question... But may I add a little more?
You see, how fast something goes is a function of its weight, or mass, and the impulsing force.... The speed of sound is limited by its great weight.... After all, the very term "Heavy Metal" music comes about because of recognition of this facet.... and, in fact, "Heavy Metal" music is known to travel slower that a "Light Aire"....
The speed of light is all but unlimited due to it lightness... and, in fact, the very word "light" is a reflection of early scientists noting the extremely-fast velocity of the stuff.... and they gave the phenomenon that name ("light") to reflect that the stuff hardly weighed anything, at all....
So, that's a bit more of the details.....
Light-waves are waves in the ether; sound waves are waves in the air. Ether is much more elastic than air, so waves travel far faster through it- about 900,000 times faster.
The speed that sounds travels at depends on the density of the air, which in turn depends on the temperature of the air. Thus, sound travels at a lower rate of speed than light, depending on the temperature, unless it is extremely hot outside
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