Note that an equipotential region might be referred as being 'of equipotential' or simply be called 'an equipotential'.
For scalar potentials, the gradient in an equipotential region is zero, since there is no change in the value of the potential. This is important in physics because the force on a body is often determined by the gradient of that force's potential function.
For example, there is zero electric field in an equipotential region (that is, a region of constant voltage). A charged particle in such a region experiences no electric force. Thus, there is no electric current between two points of equal voltage because there is no force driving the electrons.
Interestingly, ignoring local variations in altitude due to geology, the Earth's surface is an equipotential surface in the shape of an oblate spheroid due to its rotation and the Earth's gravity, and this fact allows calculation of its shape. That this is an equipotential may be easily seen, since if it were not so, the oceans and indeed the landmasses (which are subject to motion due to plate tectonics) would move so as to even out the potential.
For more information, see the general article about potential