Maps are metaphors for distortion and the Platonic chasm between ideas and representations of them. Out there in ideal world is a sphere with things at different places on it. But spheres are buggers to work with, and we can’t readily make paper maps with the same curvature as the section of the earth they represent. So we stretch and distort this ideal conception of the world to make it fit on a flat piece of paper; we project the globe onto a flat sheet of paper. In doing so we create illusions, misrepresent the real world, and mislead the reader. There are many projections (functions mapping the sphere onto the rectangle), each with its own advantages and disadvantages.
The classic illusion is the size of Greenland on the Mercator projection, the view of the world we’re all used to seeing. Greenland is not really bigger than the USA, it’s just a byproduct of the function used to map each point on the sphere to a point on the page. The Mercator projection preserves angles, making it useful to navigators, but it does so at the expense of accurately representing areas.
Other projections, such as the Gall Orthographic, preserve area. There are all sorts of variations on preservation, as map makers attempted to get specific benefits or to approximate the benefits of both (angles and areas are preserved for a particular piece of the map even though they’re inaccurate elsewhere). Projections are part of the cartographer’s art, and are beautiful to contemplate.
For that reason, I commend to you A Gallery of Map Projections. For maximum pleasure you’ll combine it with a trip through Wikipedia’s entries on Equal Area projection and Mercator projection. Enjoy, and to the club of peoplel who can never again see a map without checking the fine print to see what projection it employs.