Deformations are the result of an object’s (polygon mesh) vertices being modified in space by an external (to the object) deformer, such as a joint chain, FFD lattice, and so on. The corners of each polygon under the influence of the deformer can be translated (moved) or rotated by the deformer, and the polygons attached to the vertices will follow. Deformations allow the animator to impart a sense of life into an object mesh, and are essential to most forms of animation.
That said, deformations are also extremely useful for modeling. Often it is easier to build a simple shape, and use the deformers to conform the shape into the desired form.
Deformers can also be shaders and procedural effects such as scripts that can further modify the vertices of an object mesh. Many of the tools within Cinema 4D use this technique and driven by mathematical equations to produce useful results.