What is projection as it applies to maps

Projection is a 3D display of earth from above, it is the scientific method of depicting the earth surface on a pieces of paper that is 2 dimensional in nature as explained by your text.

Explanation:

Projections on a map help to identify the various details that one would expect to find on the real earth. Cartographers have invented this method so that depicts the  

1. Shape

2. Direction

3. Area/ size

4. Distance

All projection"s have been made based on the above data and they may be classified as high altitude, middle altitude, and low altitude. Distortions can also occur in projections and these have to be corrected from point to point. Such as the distortions indicated in Mercator's projection of Greenland.

The projection preserving direction is Azimuthal,  preserving shape is orthomorphic, preserving area is equivalent, preserving direction or shortest route is genomic projection. Projection by surface area is cylinder, cone, and sphere.

Other types are Robinson and Pseudocylindrical etc.