A geoid is an equipotential surface which (approximately) coincides with the mean ocean surface. It is often referred to as a close representation or physical model of the figure of the Earth. According to C.F. Gauss, it is the "mathematical figure of the Earth", in fact, of the gravity field. It is that equipotential surface (surface of fixed potential value) which coincides on average with mean sea level.
The geoid surface is irregular and therefore too difficult to use in mathematical calculations. For this reason, geodesists use a reference ellipsoid that approximates the volume of the geoid in their calculations.