Form is three-dimensional shape, either in reality (in sculpture) or in illusion (in painting, drawing, photography, etc).
Much attention is paid to the development in the Renaissance of convincing illusions of depth. This lends figures a greater sense of three-dimensional form than figures generally had in the anti-naturalistic, highly abstracted art of much of the Middle Ages.
Look at how Raphael creates an illusion of three-dimensional form in his La Donna Velata, from ca. 1515. Compare this with a detail of a page of the wonderful Lindisfarne Gospels, ca. 700. Both images show a head and torso of a person in voluminous robes, looking out at us, but here, the differences end. Raphael’s figure is lit softly, creating highlights and shadows that create a sense of roundness and weight to her form and clothes. The figure from the Lindisfarne Gospels, on the other hand, is almost totally flat. There is no shading to his form and the folds on his clothes are purely schematic patterns.