I think I'm saying something more fundamental than "the number isn't important", though it's true I was a bit terse. The thing a layman needs to know about c in order to understand this is that it isn't a measurement of speed as we're used to thinking about it, but a fundamental relationship between time and space in our universe.

It does measure something we can quantify in units that make intuitive sense: it is the smallest possible distance per the smallest possible time. c is not arbitrarily that; it is the fact that ties those two dimensions into a single universe, without which they would not have anything to do with each other, and without which the concepts of time and distance individually wouldn't mean anything to us.

Is that a little clearer? I'll agree it's not possible to really grok this stuff without at least doing a bunch of reading on Wikipedia.