A Mercator projection (ed: is a Conformal map, but) it also greatly distorts both angles and shapes as you approach the poles. The trivial example is to walk a square mile (N,W,S,E) you would expect the opposite sides to be at 45deg angle, but on Mercator the sides get stretched so a square in the real world can have a 10+:1 or even 100:1 side lengths on a Mercator map.
The property they both preserve is points north, south, east, or west of them on a globe are also north, south, east, or west of them in the projection. (Plenty of rectangular projections don't have this property ex: http://geographer-at-large.blogspot.com/2011/08/fun-with-map...)
The issue is interior angels of a triangle on a sphere don't add up to 180 degrees so you literally can't preserve all angles on a projection.
PS: If you actually walk exactly 1 mile north, 1 mile west, 1 mile south, then 1 mile east you don't necessarily end up on exactly the same place on a globe. (It does work if you start half a mile below the equator.)
Edit: Not that the earth is even a sphere...
