Our principal focus of relativity has to do with measurements of events where and when they happen, and by how much any two events are separated in space and in time. In addition, relativity has to do with transforming such measurements and others between reference frames that move relative to each other (Hence the name relativity).
Transformations and moving reference frames were well understood and quite routine to physicists in 1905. Then Albert Einstein published his special theory of relativity. The adjective special means that the theory deals only with inertial reference frames, which are frames in which Newton's laws are valid. This means that the fames do not accelerate; instead they can move only at constant velocities relative to one another. (Einstein's general theory of relativity treats the more challenging situation in which reference frames accelerate; the term relativity implies only inertial reference frames.)
Starting with two deceivingly simple postulates, Einstein stunned the scientific world by showing that the old ideas about relativity were wrong, even though everyone was so accustomed to them that they seemed to be unquestionable common sense. This supposed common sense, however, was derived from experience only with things that move rather slowly. Einstein's relativity, which turns out to be correct for all possible speeds, predicted many effects that were, at first study, bizarre because no one had experienced them.
In particular, Einstein demonstrated that space and time are entangled that is, the time between two events depends on how far apart they occur, and vice versa. Also, the entanglement is different for observers who move relative to each other One result is that time does not pass at a fixed rate, as if it were ticked off with mechanical regularity on some master grandfather clock that controls the universe. Rather, that rate is adjustable: Relative motion can change the rate at which time passes. Prior to 1905, no one but a few daydreamers would have thought that. Now engineers and scientists take it for granted because their experience with special relativity has reshaped their common sense. Special relativity has the reputation of being difficult. It is not difficult mathematically, at least not here. However, it is difficult in that we must be very careful about who measures what about an event and just how that measurement is made and it can be difficult because it can contradict experience.