Classical balance requires equal measure on each side of a central figure or object as well as the top and bottom. For example, in the painting "Madonna di San Sisto" by Raphael Sanzio (below) you can see that the central figure (Madonna and Christ) are balanced by the two other figures on the left (Saint Sixtus) and right (Saint Barbara) as well as the two cherub below (on the bottom edge of the picture). Classical balance gives the painting equal balance across the entire image.
If you were to visualize the painting as a scale, it would look like the image below. If you notice both items on each side of the scale are equal in weight. So you can say that it's perfectly balanced. For each item in the painting above, there must be a corresponding element that keeps the balance from tipping. One thing to remember is that every item in a picture has a degree of pulling power, much like a magnet. While each piece draws attention to itself, it takes away from every other item proportionately.
In the image above, "Coronation of the Virgin" by Diego Velazquez, notice how he uses classical balance to compose the painting. All of the elements that surround the Virgin Mary are equally balanced on the right and left as well as the top and bottom.