The contrapposto figure is one of the most important developments in European sculpture.
First of all, to understand what contrapposto is, you have to understand what it isn't. Take, for example, the artwork of Ancient Egypt. The Egyptians, though they were incredible stoneworkers, viewed sculpture as only a foreboding extension of their wall carvings and architecture, built to form with the structures around it and best viewed from only certain vantage points. Like their paintings-- so many of which were dominated by figures shown in severe profile instead of natural perspective-- a lot of their sculpture also had a kind of two-dimensionality to it, lacking in any real motion or depth.
In the earliest Greek sculpture, from the 5th and 6th centuries BCE, you can clearly see the heavy influence of the archaic Egyptian style. However, starting in the late-5th century BC and culminating in the Classical Greek period of 4th, the cunning Athenians discover contrapposto and everything changes.
Now, portraying the human form in a natural posture is probably something you'd take for granted. It's actually a lot more complicated than you might think. Sculpting contrapposto figures requires an intricate understanding of geometry and anatomy. Their mastery of the technique was perhaps the most visible sign of the tremendous advancement of Greek civilization over the Assyrians and Egyptians.
At the same time, contrapposto posing changed the way the medium itself was viewed. It put forward the concept of "sculpting in the round", where each sculpture is designed as a free-standing and independent work of art, to be admired for its own balance and beauty. The subtle twisting of the form encourages viewers to walk around the piece and enjoy it from many angles (a trend that can be traced directly into our post-modern styles of "installation art").
Notably, though it was lost somewhat in the "Dark Ages" of Europe's medieval era, the Italians brought back the contrapposto style with a vengeance during the Renaissance, as part of their new-found interests in naturalism and ancient cultures.
One obvious example of contrapposto be Michelangelo's David. An even better one, perhaps, would be the Niches of Or San Michele in Florence.
These 14 niches were commissioned by the most powerful trade guilds in 15th-century Italy, then constructed in the years 1410-1430 by dozens of the best Florentine artists that money could buy, including the likes of Donatello di Betto Bardi, Lorenzo Ghiberti and Nanni Di Banco. Amazingly, despite it being quite early-on in terms of the Renaissance, each of the massive, carved-marble figures shows a common and fairly advanced form of contrapposto positioning.
Di Banco's niche, one of the first completed, shows four saints who were martyred during the days of the Roman Empire, comfortably standing in an open half-circle as if engaged in an animated discussion and waiting for you to butt in. Definitely a huge departure from the austere and sanctimonious style of the previous era.
Donatello's statue of St. Mark, for the Weavers' Guild, is even better. The old master sculpts Mark into an exaggerated contrapposto posture, leaning heavily on his right leg, his book tucked under his arm and staring off into space. The pose is unbelievably honest. It makes it seem like the saint is almost bored, as if at any moment he's about to say "Dammit, Donatello! Are we almost done here? I've been standing on this fricking pedestal all day, and I've got a whole pile of important, saintly stuff I should be doing right now."
And, at least to me, that is what contrapposto is all about.