For an object in orbit around the earth, the apogee is the point that is highest or farthest from the earth. Early satellites had low apogees, so it wasn’t long before they burnt up in the atmosphere.
Apogee comes from two Greek words meaning “away” and “earth,” so it’s specific to things orbiting the earth. If you’re talking about something orbiting the sun, the equivalent word is aphelion, “away” + “sun." Because apogee denotes the highest point something reaches in an orbit before falling back, it can also figuratively refer to other highs. For example, "Child stars sometimes reach their apogee by 20, and there's nowhere to go but down from there."