Borrowing two phrases from Herman Bondi, we can catch the spirit of Einstein's two postulates by labeling them: (1) the principle of the irrelevance of velocity and (2) the principle of the uniqueness of light. In what senses are velocity irrelevant and light unique in these two statements?

In accordance to Einstein’s first postulate of special theory of relativity, the fundamental laws of physics have the same form for all inertial reference frames. But according to second postulate, the speed of light in free space has the same value c in all inertial reference frames that signifies that the velocity of light in vacuum is independent of the relative motion of the source and the observer.
The first postulate is the extension of the conclusion drawn from Newtonian mechanics; since velocity is not absolute, but relative which is a fact drawn from the failure of the experiments to determine the velocity of earth relative to ether. The transformation must be linear and for low speeds for v << c they should approach the Galilean transformations.