In physics, the term relativity is used in several related contexts:
* Galileo first developed the principle of relativity, being the postulate that the laws of physics should take the same form for all observers in uniform motion with respect to each other. It incorporates the classical view that time is universally the same for all such observers. The same principle holds in Newtonian mechanics.
* Einstein's theory of relativity consists of special relativity and general relativity. It reshaped the classical view, arguing that time is relative to the observer, in an analogous way to position in space. There is ample experimental evidence that this is indeed the case, however paradoxical the implications may appear.
Galileo's relativity principle can be viewed as a very accurate approximation at velocities small compared to the speed of light in vacuum. This accounts for the widespread validity of so-called "non-relativistic" mechanics, in such circumstances. However, strictly speaking, Newtonian mechanics is also relativistic, in that Galilean relativity incorporates many of the essential features of relativity.
The physical reason that Einstein relativity took over from Galilean relativity is basically that it is a more general framework, which includes the previous theories of mechanics as a limiting case, for small velocities.
http://en.wikipedia.org/wiki/Relativity