Area

An equal area map preserves the property of area. This means that the total area of the map is the same as the total surface area of the earth (once scale is taken into account). It also means that any expanse you mark off on the earth's surface will have the same area on the map, although the shape of that expanse will most likely change.

In the graphic below, two circles on a sphere are projected onto an equal area map. One remains a circle (it got lucky and was projected to a point of no distortion) and the other is distorted into an ellipse. The important thing is that both projected shapes have the same area as the original circles.

Two circles on a sphere are projected to the corresponding locations on an equal area map.

Here's a way to think about it mathematically: the major and minor axes of a circle are equal in length. When a circle on the earth is projected into an ellipse on a map, one axis becomes longer than the other. As long as the total length of the axes doesn't change, however, the ellipse keeps the same area as the circle.