What is special about special theory of relativity?

Relativity was a concept in physics before Einstein came along. Galileo wrote about "The Basic Principle of Relativity". So "Special Relativity" refers to relativity applied to the special case of light beams (and spacetime)--the study of which Galileo was not equipped to tackle, since in his time the speed of light had not even been determined (although later it became clear that there had been some data laying around).
Einstein's General Theory of Relativity attempted to wrap up this "relativity" thing by including the theory of space curvature being the reason for gravity.
Einstein could just as well have called them "Relativity" and "Relativity The Sequel".