Shapes are two-dimensional, forms are three-dimensional. Cubes, pyramids, cones, and spheres possess depth and therefore volume. Any structure or building has volume, but so do their interiors. Anything that has four or more connecting planes that create a form has volume. This can also be literal or implied in the way planes and lines are used to create the form in question. Perceived volume can be as effectual as actual volume in a space, and depends on the intended use or desired atmosphere.
|Image credit: Kleinman, Susan. "Mid-Country Modern." Metropolitan Home. April 2006. 105. (Overlay mine.)|
Volumes can push out or enclose, and clever usage goes a long way to creating an effective and beautiful design.