[modarts]

Maxwell's equations were not "written down to explain it to someone who doesn't already know what it means". They, quite simply were written down to express relationships between the motion of charge, and the behavior of electric and magnetic fields as a consequence.

You have to understand the physics behind the equations (what's charge? what's an electric field) as well as the mathematical structure (what's a vector space? what's a line integral?) in order to make use of them. They are equations used to answer questions like "What happens to the strength of this magnetic field if I increase the velocity of this charged particle responsible for generating it"? They aren't meant to be explanatory (but have the beautiful side-effect of explaining how light propagates in a vacuum.)