You’ve definitely seen shapes and/or forms before, because they are everywhere. They are, in fact, an integral part of the conceptual framework that our brains use to identify objects. Forms can be free form, organic, naturalistic, geometric, lifelike, exciting, sad, aerodynamic, symbolic (think letters...), and many other things our brains assign them. But forms can also be entirely abstract, as the Greeks (Euclid included) used to think of them: perfect forms, existing only in abstract thought, from which all physical forms were (imperfectly) derived.

But even the most abstract shapes in the visual arts have some objective qualities. Case in point, Malevich’s referred to his 1915 piece Black Square as the "zero point of painting¹," meaning that, other paint on canvas, it was nothing: just near-complete abstraction. Yet despite this high-minded rhetoric, it's chock full of objective elements, so it can still be referred to as a rectilinear shape that is dark black (value) and, at the time of this writing, has a crackled patina (texture).

Form

In two-dimensional design, forms are similar to shapes, in that they are actually two dimensional, but appear to be three dimensional, as seen below. If you've even created or seen a still life painting, you know what a form is!