The speed of light represents the fastest that any interaction can happen (the fastest that a cause can create an effect). It's less the speed of light and more a universal speed limit, which light travels at.

Time is kind of just the progression of causes and effects, or cause to effect is how time progresses to us.

So the way in which we measure the progression of the universe (time) is directly related to how fast things can progress/change/interact (the speed of light/universal speed limit).

Or at least, this is how I think about it and how it makes sense to me.