The numerical value is determined empirically, and as far as I know it is simply a result of our historical choice of length and time units.
The fact that there is a definite speed of light is also a property of nature but there is some "explanation". We know that space and time mix. When you speak of an event you need to state both position and time. When you speak about two events, you need to tell their relative position and time difference as well as a reference frame (by indicating its velocity). This separation of events in space and time will be different for different observers, if they are moving at different speeds. The way you transform this quantity includes a constant. When you write the equations governing the electromagnetic phenomena and require that the results obey these transformation rules, it turns out that this constant is the speed of the electromagnetic waves, which is of course light.
The event separation transformation rule dictates that no information can be transferred faster than this constant, the speed of light. Otherwise you can have two events A & B, where the A can influence B in one reference frame and B can influence A in another reference frame. This would lead to a contradiction.
These are explained much better in standard relativity texts. I'd recommend Rindler's "Essential Relativity" and Thorne's "Time Warps and Black Holes"'s first few chapters.
The fact that there is a definite speed of light is also a property of nature but there is some "explanation". We know that space and time mix. When you speak of an event you need to state both position and time. When you speak about two events, you need to tell their relative position and time difference as well as a reference frame (by indicating its velocity). This separation of events in space and time will be different for different observers, if they are moving at different speeds. The way you transform this quantity includes a constant. When you write the equations governing the electromagnetic phenomena and require that the results obey these transformation rules, it turns out that this constant is the speed of the electromagnetic waves, which is of course light.
The event separation transformation rule dictates that no information can be transferred faster than this constant, the speed of light. Otherwise you can have two events A & B, where the A can influence B in one reference frame and B can influence A in another reference frame. This would lead to a contradiction.
These are explained much better in standard relativity texts. I'd recommend Rindler's "Essential Relativity" and Thorne's "Time Warps and Black Holes"'s first few chapters.