The far field is the region far from the antenna, as you might suspect. In this region, the radiation pattern does not change shape with distance (although the fields still die off as 1/R, the power density dies off as 1/R^2). Also, this region is dominated by radiated fields, with the E- and H-fields orthogonal to each other and the direction of propagation as with plane waves.
If the maximum linear dimension of an antenna is D, then the following 3 conditions must all be satisfied to be in the far field region