The geoid is a visual representation of the Earth's profile. It is made by creating a hypothetical ideal sea level that would cover the entire planet, extending under most land masses. It is not a representation of mean or average sea level where the surface of the Earth would be totally flat and covered in water, because the planet itself is not flat. Viewed in cross section, the geoid has a number of dips and peaks that correspond to changes in the Earth's mass.
There are a number of ways to visualize the Earth's surface for convenience when making maps and charts. The Earth is not perfectly round, but has a more elliptical shape. Some resources use the reference ellipsoid, which pretends the surface of the Earth is flat. Others may look at the topography of the Earth, or the average sea level. None of these representations provide a completely accurate image of what the planet's surface and shape look like.
Sea level is not constant worldwide; individual oceans can be higher and lower and have variations across their surfaces. This is exaggerated with the influence of tides and other factors. To determine the shape of the geoid, researchers pretend that the Earth is covered in water, and take note of points where it would be higher or lower. On land, this falls below the topography, as the ocean couldn't extend to cover a mountain range. Areas with higher mass, like mountains, would force the water to bulge, while deep valleys have less gravitational attraction and would cause a dip.
Viewed in cross section, the geoid shows a series of gentle peaks and troughs which illustrate the way the Earth's gravitational field behaves in different regions. It doesn't represent the gravitational field itself, but what would happen if water covered the Earth, or, more realistically, if deep trenches were cut across the continents to allow the ocean to flow inland. The water in these trenches would change elevations as it crossed the geoid.
Charts illustrating the difference between topography, reference ellipse, and geoid are available. These show that the reference ellipse can be highly inadequate for things like elevation measurements, as it may like considerably higher or lower than the actual topography. The geoid corresponds roughly with features like mountains, but does not take on such extreme elevations and dips. This information can be important for tasks like using a global positioning satellite to fix a location.
