Mark Gimein has a good post about Special Relativity, that makes some excellent points:
That it could just as easily be called the theory of constancy (of the speed of light), and that the best way to read about it is from Einstein’s own layman’s explanation.
But more than that, that it is a theory of a flexible space and time background, introduced to resolve the impossibility of both (a) the summed relative motion (i.e. non fixed speed) of objects to or from light beams and (b) the (always observed) fixed speed of objects to or from light beams when measured against (c) the same fixed, universal co-ordinate system (clocks and measuring sticks).
Instead of ditching (a) or (b), Einstein ditched (c).
(a) was proven mathematically, (b) was proven by observation and (c) was assumed as obvious common sense based on experience.
Special relativity is a triumph of science over the senses and never trusting instinct, yet the Einstein myth sometimes creates the idea of the opposite - of following intuitive hunches. Yes, but only if they could be backed up with evidence. His creative thinking should not be confused with quasi-spiritual or artistic acceptance of intuition without reason.
Summed relative motion is obvious (two trains travel towards each other at their combined speed) and constancy of speed of light is empirically proven, therefore the insight Einstein had was to reconsider what seemed immutable - the fixed background of space and time.
Or was it? Einstein was taught by Lorentz and the idea of spatial contraction (admittedly, of objects not the space itself) to resolve the speed of light paradox was principally his. Like all things the truth is less clean than the fable. Special relativity was a conceptual breakthrough (principally in the linking of space and time), but still part of a continuum of thought.
Anyway. Mark’s post is a really good digest of the background of Special Relativity in qualitative terms: see here.