A better name for "the speed of light" might actually be "the speed of time" or "the speed of information transfer".

It's a mathematical limit and you can derive it using pretty much anything, not just light.

As an object goes faster, it experiences time dilation, length contraction, etc. The "Speed of Light" C is basically the point at which all of these things reach either zero or infinity.

It also "just so happens" that electromagnetic waves (such as light) travel at exactly this speed in a vacuum. They travel that fast because they travel at the maximum possible speed, and that happens to be the maximum possible speed.

It's like if you always traveled at the speed limit because you didn't want to break the law, and we called it "triplesex_ speed", but really it's just the maximum speed that anyone would go if they didn't want to break the law.

Except in this case it's not just a law- it is (to the best of our knowledge) physically impossible to go faster. It's not just that we haven't seen anything go that fast- it's that going faster than that doesn't even really make sense theoretically - for example, it would result in time-travel (this has to do with the fact that the order in which events happen and the speed at which time passes is different to different observers depending on the speed at which you're traveling).