Why do we find a large number of nude male characters in ancient Greek paintings and sculptures? What was the social status of nudity in ancient Greece?
The Metropolitan Museum of Art in New York has a great page on this exact topic. The key ideas why there is so much male nudity are two-fold:
Because the Greeks felt that sport was such an important part of what was good about humanity, and male competitors embodied that idea, they sought to capture it in their art work. Later on when the Renaissance masters came along they emulated those themes.
As far as the social status of nudity in Ancient Greece the reality is a little unclear. People were likely not nude in public all the time, but they may have been some of the time as this article pointed out.
So, in summary, male nudity in art was revered, and actual nudity in public was probably limited.
I have dealt with this question in my article, "Nudity as a Costume in Classical Art," in American Journal of Archaeology 1989, which can be accessed either through JSTOR or through Academia.com, under my name. I am also editing a multi-author book, Nudity as a Costume in the Ancient Mediterranean, where I take up the subject of Greek nudity again.
The answer to your question is that the naked kouros, and the Greek athlete, were citizens. Nudity was confined to the exercise ground, where the young men prepared for war. Only citizens served in the army, so basically male nudity was a sign of citizenship. Slaves were also shown nude, but they were shown as ugly as misshapen, not the image of the kalos kagathos, "beautiful and noble" young citizens of Athens.
There is yet another reason why the male nude was common in Greece.
The Greeks were obsessed with perfect proportions in all of their art, for they saw these proportions as a sign of the divine cosmos. Perhaps the most notable of these monuments is the Parthenon and its Golden Mean ratios, a temple dedicated to Athena which, very clearly links perfect proportions to the divine. This ideology permeated everything in Greek culture and philosophy. Think, for example, of Pythagoras and his discovery of musical intervals and their perfect proportions, or the so called Platonic solids.
The human body inherently is a study in the Golden Mean. All of the limbs of the body adhere to some form of Golden Mean ratio and the Greeks knew this. Greek statues were there to celebrate the divine by exploring the perfection of the human body. Note that almost no Greek Statue (and being careful here, since many Greek statues we know are actually Roman copies of Greek originals) shows a body that is not perfect. Also note that any garment that covers the body will be human made and thus not part of the divine. To see divine creation you must draw the nude.
Now combine this with the subject matter of Greek statues which, are typically mythical heroes or heroines and gods and goddesses. Such perfect statues were the only way that the perfection of heroes, heroines, gods, and goddesses could be worshipped. By the word worship here I mean a celebration that includes being awed and inspired.
So basically the nude literally shows "naked perfection," and no other creation was seen as more perfect as the body of the idealized male.