According to Maxwell equations (which in turn came from Colomb inverse square law and relativity, which in turn came from 3-dimensionality of space and from symmetry of motion (all laws of physics are the same in any moving system of reference)), when electric charge is moving then due to space contraction its electric field is more dense, and we call a minor difference between field of non-moving and moving charge "magnetic field".
According to same Maxwell equations, when a charge moves with acceleration, electric field can not keep up with its motion: on large distance it still is "undisturbed", pointing to where charge is no longer is. So, there is a "transition" place where field changes from pointing to "new position" of charge to "old". Mathematically this changing e/magnetic field is what we call radiation because it moves from cahrge in all directions. Now, Maxwell equation have only ONE solution for the speed of motion of this disturbed field - c, regardless motion of charge, or observer, regardless gravity, other fields around, etc. And that is exactly what we see: speed of radiowaves, x-rays, etc. is always c even if you move toward/away ftom the source with any speed (even c!). That is why it is called constant. And because it is related to the properties of vacuum (or space-time if you wish), it is called fundamental constant (and we know only two more such constants, h and G. Elementary charge e as well as masses, spins, etc of elementary particles seem to be consequances of these 3 constants and of dimensionality of space). Anyway, because c should be the same for all observers seeing the same beam of light, then (as c=space/time) both space and time should be diggerent for each observer to keep c the same. Mathematically the only way of having c constant for all moving observers is to modify their space-time by Lorentz transformation, which results in shrinking space and time as you move, and this in turn, results in increasing of mass and energy, which in turn results in supplying infinite amount of energy to accelerate non-zero mass body to speed c. (Speed of zero-mass bodies is always c. That is why photon dies if you stop it - there is no solution of Maxwell equation with the speed NOT equal to c.) Anyway, if you can supply MORE than infinite amount of energy to accelerated body, then you can make it move faster than light.