Geoid is an equipotential surface.

Actually, if you look at it from space you probably won't see the side-to-side anomalies because they are relatively small compare to the ellipsoidal one. But if you'd put on 'magic glasses' which enhance the anomalies relative to the Earth radius, that's what you'd see from the space! The North pole is up. The black vertical line cuts along Greenwich.

Here we took off the ellipticity (as due to the Earth rotation), and displayed the Geoid Anomalies using interrupted Hammer-Aitoff projection with the continents sketched with white line on the background.

Those density contrasts drive the mantle flow: the lighter rocks flow up and the denser ones sink down, very-very slowly.

Imagine a slice through the Earth, as in picture on right. The dark gray is inner core: greatly hot-pressed solid metallic ball. The light gray is outer core: hot but not as greatly pressed as the inner core material - and therefore it's in a liquid state, giggling and convecting at high rates of several km per year (some places reaching 10-20 km/year!! - it's like 2 meters in hour). Above is the mostly silicate rock mantle (white layer in picture, although most abundant rock in upper 600-km of mantle looks like light-green glass). The mantle creeps very slow (about couple centimeters per year) driven by the gravitationally unstable blocks of rocks. Light-density, hotter rocks are colored reddish here and the heavier (cooler) chunks are bluish.
Since mantle is extremely viscous (on geological time scales), its flow causes topography at all outer boundaries (surface, which is covered with the blue ocean, and the core-mantle boundary).

Here I illustrate how the equipotential surface reacts to the changes in the rheology of the media surrounding a mass anomaly:

Let's consider 2D-Cartesian geometry, for simplicity. When no mass anomaly is present in the media (mantle), the equipotential surface is flat (here it's called a reference equipotential surface and is shown by black line)	Now we add a heavy mass anomaly. In a rigid media (we do not allow any motion) it causes a 'cavity' in the gravitational potential field, so it shows up as a bulge in the equipotential surface: positive geoid anomaly (blue line)
Holding the mass anomaly still, we allow the media to respond to the change in the gravitational field: its free upper surface would be pulled up to equilibrate (to line up) with the equpotential level (effect of self-gravitation). Thus created topography (I call it secondary mass anomaly) would re-adjust the potential field (and geoid, green line).	Now we let the mass anomaly to sink down. The viscous stresses of the generated flow pull the upper boundary down creating another secondary mass anomaly (so called dynamic topography) which is, by the way, has an opposite sign (lack of mass at the surface) and causes an opposite-sign (negative) anomaly of the geoid (magenta line).