1. The point in the orbit of the moon or of an artificial satellite most distant from the center of the earth.
2. The point in an orbit most distant from the body being orbited.
3. The farthest or highest point; the apex: "The golden age of American sail, which began with the fast clipper ships in 1848, reached its apogee in the Gold Rush years" (Los Angeles Times)
Above retrieved from Answers.com
It is the point in the orbit of the moon or of an artificial satellite most distant from the center. So when the moon is at it's farthest point from the Earth, that is it's apogee. The closest point, by the way, is called the perigee.