A geoid is a mathematical object exactly representing the
Earth's surface, with all of its bumps and divots.
In
geodesy, the geoid is more carefully defined: This is an
equipotential surface representing
mean sea level around the Earth. This is not
quite the same as an
ellipsoid: There are all sorts of
anomalies in the Earth's gravity field, caused by
continents among other things, each of which affects the shape of the geoid. The Earth is sort of
pear-shaped.