Geographic projections are a way of showing the curved surface of the Earth on a flat surface like a piece of paper...
From the Manifold user documentationManifold user documentation:
Earth is not an exact ellipsoid. In fact, because the Earth is such a "lumpy" ellipsoid no single smooth ellipsoid will provide a perfect reference surface for the entire Earth. The practical solution to this is to measure the Earth's shape in different areas and to then create different reference ellipsoids used for mapping different regions on Earth. A datum is a reference ellipsoid together with an offset from the center of the Earth. By specifying different offsets, you can use the same standard ellipsoids in many different regions of the Earth. Different countries will often use the same ellipsoid but with different offsets for standard government maps in those countries.