An inertial reference frame is a reference frame in which the first law of classical mechanics holds: A body on which no external forces act either remains at rest or moves with constant speed along a straight path. An inertial observer is an observer that is at rest with respect to an inertial reference frame. In the context of relativity, an inertial reference frame is one that drifts in gravity-free space without undergoing rotation or being accelerated.
Inertial reference frames play a central role in special relativity: the basic postulates of that theory are the relativity principle (which holds that the laws of physics are the same in all inertial reference frames – no such frame is special, in this sense) and the postulate that the speed of light has the same value for every inertial observer.
In general relativity, there are no real inertial observers, however, by what’s called the equivalence principle, the laws of physics for an observer that is in free fall and performs his measurements only in his direct neighbourhood (and only over a limited period of time), the laws of physics are approximately the same as for an inertial observer.