Let's pretend for a moment that we don't have to worry about gravity and all the General Relativistic effects that entails. Einstein proposed that one could imagine a physical realization of a reference system by building a lattice of clocks. One would make the lattice spacings equal everywhere by using standardized sticks. One would synchronize the clocks by sending signals back and forth between them, making the assumption that light travels at equal speeds in all directions, i.e. that Maxwell's equations are true. All four coordinates of any event are obtained by interpolation between the nearest clock ticks of the nearest clocks.
Now if it is possible to construct one such coordinate system, it is possible to construct others in motion with respect to the first one. The Lorentz transforms of Special Relativity are simply the recipe for translating from the coordinates of one such system to those of another. It turns out that if gravity is present, the clocks don't stay synchronized and other peculiar effects occur, such as distances not obeying Euclidean geometry. In that case the solution turns out not to be to consider a narrower set of coordinate systems, but rather a much broader set but with more complicated laws.
(republished on 07/23/06)