Original by Philip Gibbs 1997.
One answer is that it isn't. When physicists work out equations in relativity they often set the speed of light to one: c = 1. This makes the equations more tidy. It amounts to defining natural units of measurement in which the speed of light is exactly one unit. For example, if the second is kept as the basic unit of time, then the unit of length must be equal to exactly 299792458 metres. This unit is called the light-second because it is the distance travelled by light in one second. The speed of light is then one light-second per second.
This is not a complete answer. The speed of light is high when measured in our standard units such as metres per second or miles per hour. Those units are defined by arbitrary conventions which have their roots in ancient ways of keeping time and measuring distances. It is probably no accident that the second is about the average duration of a heart beat and the metre or yard is the distance of one human step. So the real question is "Why is the speed of light so high in terms of familiar every day measurements?" or "Why are the speeds at which we normally move so slow compared to the natural units in which the equations of physics take the most tidy form?"
These are very meaningful questions but ones to which we have only partial answers. The speeds at which we walk and live are limited by the amounts of energy E available to us from the chemical processes which drive our muscles compared to the amount of mass m which is to be moved. Kinetic energy at low speed is given by the formula E=(1/2)mv2. So the order of magnitude of velocities we obtain when powered by chemical energy might be given by the square root of E/m. Actually it will be much less than that because we are very inefficient in our use of energy, allowing most of it to be released slowly and dissipated as heat. Our speeds might also be related to the strength of gravity on Earth g = 9.81m/s2 in relation to our own size. It is no coincidence that g takes a moderate value in conventional units, unlike c.
It is a consequence of relativity deduced by Einstein that the amount of energy available from a mass m is given by E = mc2 so the question now becomes (in part at least) "Why is so little of the energy of matter available in the form of chemical energy?" If our metabolisms worked using nuclear reactions instead of chemical reactions we might move much faster (other factors permitting) and then our units of length and time would be different, and the speed of light would not seem so high. These relative scales of energy are determined by such parameters as the coupling constants of the natural forces and the masses of particles. We know from observation that these take values which vary widely in scale over many orders of magnitude. We do not yet know why this is. It may be that the values are arbitrary and their differing values have to be put down to something ontological such as the anthropic principle, or it may be that they are determined without ambiguity from a unified theory of forces which split naturally at different scales. The strength of gravity on Earth comes from similar parameters in cosmology and similar principles may apply to the question of why hospitable planets have moderate gravitational fields. Until more is known about the fundamental parameters and how they derive from deeper principles, a complete answer cannot be given.