Classical Greek sculpture was made to almost solely embody this deal of Man being the measure of all things. In fact, The Doryphoros (Spear Bearer) by Polykleitos, was made as a physical model of this exact idea. Polykleitos wrote a book called The Canon that discussed how to create the perfectly proportioned sculpture, and then sculpted The Doryphoros as a visual aid so that one could see the exact proportions he wrote about. Furthermore, man was seen as the measure of all things because he was the closest in form to the Ideal form, or one could say godly form. Going back to Plato, many Greeks believed in this Ideal Form. The basic idea was that everything on earth was a sort of poor copy of an original, ideal form (so the chair you are sitting in is A chair, but it is not THE chair - that would be the ideal form). Because man was rational, he was closer to the gods and thus the ideal form. And since no man is totally ideal or perfect, the Greek artists decided to make a form of man that was as close to perfect as they could get, such as Polykleitos' Doryphoros. The heroic nude form was also chosen because it highlighted the ideal parts of man: heroism, athleticism, rationality, and beauty. Unlike today's Western society, Greeks thought the male form was the most beautiful - not the female (most females were shown clothed unless they were goddesses).
Thus, man is the measure of all things because, since he is rational, man does actually measure all things. But more importantly, (heroic, perfectly proportioned, nude) man is the measure of all things because he is the closest to Ideal, or god-like) anything can get. So the closer you are to Ideal Man, the closer you are to perfection. In fact, even though The Canon no longer exists, many art historians believe Polykleitos chose to head as the unit to base the rest of the perfect proportions around (so the chest should be X number of heads tall, etc) because it is the seat of the mind/reason.