Inertial frame of reference
In physics, an inertial frame of reference, or inertial frame for short, is a frame of reference in which the observers move without the influence of any accelerating or decelerating force.
If you can find an inertial frame of reference for a given situation, then it can always be transformed by a change of coordinates into one in which the observers do not move at all.
The transformation from one inertial frame of reference to another is done using Lorentz transformations, or, at speeds considerably below the speed of light, Galilean transformations.
An inertial reference frame is a space-time coordinate system that neither rotates nor accelerates. In real life, such frames of reference are purely theoretical, because gravitational force (and thus acceleration) exists everywhere in the known universe. However, they may be approximated very well in intergalactic space, or to a lesser extent within the confines of a coasting spacecraft.
Inertial frames of reference appear prominently in both Newtonian relativity and Einstein's special theory of relativity.
In Newtonian mechanics, any mass viewed from an inertial reference frame will appear either to be stationary or to be moving at constant speed in a straight line, if and only if the sum of forces acting upon that mass is zero. (This is also known as Newton's first law of motion.)
Different inertial reference frames may have different origins at any given moment in time, and their respective origins may be moving at constant speed and direction relative to each other. An object which is stationary in one inertial frame will also appear to be stationary in another inertial frame. A non-inertial frame of reference is a coordinate system which is accelerating.
Correction:
It is not satisfactory to define an inertial frame as above: rotate or accelerate with respect to what? In the context of Newtonian mechanics we can define an inertial frame as one in which Newton's laws hold. (Note that the question of whether a frame is inertial requires us to decide what forces are acting; strictly speaking there is no absolute means of determining whether or not a frame is inertial, for additional forces can always be postulated to explain behaviour that seems to show the frame is non-inertial. In practice, we are agreed on when to say a body is free of external influence because we are largely agreed on the conditions for the action of the various forces that enter our physical picture of the world.) It is a simple consequence of this definition and the laws that all members of the family of inertial frames move with constant velocity with respect to each other. An object stationary in one inertial frame need not appear stationary in another but will move at constant velocity in that frame. (NB: the claim above that such frames are 'purely theoretical' is rather confusing as a reference frame is evidently an abstract entity in any case. Presumably what is meant is that few moving bodies (eg the earth) yield an inertial coordinate system when we locate our origin on, and orient our axes with respect to, them.)