Form refers to three dimensional objects. While shapes have two dimensions (height and width), forms have three dimensions (height, width and depth)
Forms that are three dimensional, such as sculptures or buildings are called real forms.
Little Dancer, Aged Fourteen (Edgar Degas, 1880 – 1881) is a real form. The sculpture takes up space and has height, width and depth.
Two dimensional work can suggest three dimensional objects by including implied forms. This means that lines or shapes are shown in a way that suggests they have depth. This can be done using perspective, or through tone or colour effects.
The blue cube in Composition (El Lissitzky, 1920) is an implied form. It appears to have a front (with width and height) and sides (adding depth).
The two different blues used suggest light hitting the cube in different ways on different sides. This adds to the 3D effect.