Start the Story Here
Get started with all this datum and coordinate stuff here.
Earth as seen from space
http://earthobservatory.nasa.gov/Features/BlueMarble/BlueMarble_history.php
Turn it into mathematical shapes and we get a Spheroid & Ellipsoid. (The terms are used interchangeably by many users. On this site Spheroid = the perfectly round ball, Ellipsoid = the ball squashed in the middle.
Realistically earth is an Ellipsoid not a Sphere. You can't see it in the picture from space due to the scale, but the earth is about 40km smaller in diameter around the poles than around the equator.
Scientists have measured sea levels and gravity around the world to figure out what the shape of the earth really looks like.
This model is created by Barthelmes & Köhler & shows gravity fields around earth. The colours indicate the undulations of the Geoid above and below the Ellipsoid. The geoid is an approximation of mean sea level and gravity.
Barthelmes, F. & Köhler, W., 2012
International Centre for Global Earth Models (ICGEM),
Journal of Geodesy, The Geodesists Handbook 2012, 86(10), 932-934.
http://icgem.gfz-potsdam.de/ICGEM/
The green shape represents the Geoid & therefore an approximation of gravity & mean sea level (the two are related).
To measure this bizarre shape we draw an Ellipsoid around it to as a best fit.
The blue lines are the lines of latitude & longitude on the ellipsoid.