Until several years later when Einstein developed general relativity, which introduced a curved spacetime to incorporate gravity, the phrase "special relativity" was not used. A translation sometimes used is "restricted relativity"; "special" really means "special case".Some of the work of Albert Einstein in special relativity is built on the earlier work by Hendrik Lorentz and Henri Poincaré. The theory became essentially complete in 1907.

The theory is "special" in that it only applies in the special case where the spacetime is "flat", that is, where the curvature of spacetime (a consequence of the energy–momentum tensor and representing gravity) is negligible.In order to correctly accommodate gravity, Einstein formulated general relativity in 1915. Special relativity, contrary to some historical descriptions, does accommodate accelerations as well as accelerating frames of reference.
What is the special aspect of Einstein's special theory of relativity?
The "special" part of Einstein's special theory of relativity is a reference to it being a special case of his General Theory of Relativity. Special relativity only applies in the special case where the curvature of spacetime is negligible, i.e., spacetime is "flat". Special relativity was formulated in 1907, and in order to correctly accommodate gravity, Einstein formulated general relativity in 1915.