(noun) - Form is one of the seven elements of art. At its most basic, a form is a three-dimensional geometrical figure (i.e.: sphere, cube, cylinder, cone, etc.), as opposed to a shape, which is two-dimensional, or flat.
In a broader sense, form, in art, means the whole of a piece's visible elements and the way those elements are united. In this context, form allows us as viewers to mentally capture the work, understand it and attempt to analyze it.
Finally, form refers to the visible elements of a piece, independent of their meaning. For example, when viewing Leonardo's Mona Lisa, the formal elements therein are: color, dimension, lines, mass, shape, etc., while the feelings of mystery and intrigue the piece evokes are informal products of the viewer's imagination.
"Sculpture is not the mere cutting of the form of anything in stone; it is the cutting of the effect of it." - John Ruskin