General relativity is just describing gravity in a relativistic setting. The equivalence principle hints to the idea that gravity is spacetime curvature.
In special relativity much attention is given to inertial frames, because they are equivalent. However, SR can perfectly handle other frames like accelerating ones, just as in Galilean relativity (classical mechanics) you can describe accelerating observers.
The key difference between classical mechanics and relativity is that, while in classical mechanics only linearly accelerating observers can locally pretend they are in a gravitational field, in GR every observer can locally pretend he/she is in a gravitational field. The class of "equivalent observers" is thereby enhanced.