Special relativity is the basis of our understanding of physical space and time. Our everyday experience is that space and time are simple and unchanging. In particular, we all experience the same space and time. We have this experience because we always move at speeds which are very slow compared to that of light (300,000 km per second).
For observers moving at, say, greater than 10% light-speed, this everyday experience is no longer found to be correct. Space and time are found to be complex, to be different for the different observers, and to stretch and mix in surprising ways. This new structure of space and time is called space-time, and the theory describing it is called "special relativity".
Einstein later discovered that gravity is also deeply related to stretching and mixing space and time. His space-time based theory of gravity is called "general relativity".