From Well, the health blog on The New York Times web site:
The push-up is the ultimate barometer of fitness. It tests the whole body, engaging muscle groups in the arms, chest, abdomen, hips and legs. It requires the body to be taut like a plank with toes and palms on the floor. The act of lifting and lowering one’s entire weight is taxing even for the very fit.
“It takes strength to do them, and it takes endurance to do a lot of them,” said Jack LaLanne, 93, the fitness pioneer who astounded television viewers in the 1950s with his fingertip push-ups. “It’s a good indication of what kind of physical condition you’re in.”
“You are just using your own body and your body’s weight,” said Steven G. Estes, a physical education professor and dean of the college of professional studies at Missouri Western State University. “If you’re going to demonstrate any kind of physical strength and power, that’s the easiest, simplest, fastest way to do it.”