That toward which an inclination, power, or operation of some kind is directed. 

Formal Object.— The aspect of a thing toward which a power, habit, or act is directed. E.g., the color of bodies is the formal object of sight, quantifiably mobile being is study the formal object of quantitative physics, being studied in its mutability is the formal object of natural philosophy, and being studied precisely as being is the formal object of metaphysics 

Material Object.— The consideration of an object of knowledge under the aspect of its concreteness, in contrast to a formal consideration of the object.  Some scholastics distinguish these two considerations by speaking of the material object as res and the formal object at obiectum.  Thus, for example, God, who is one in res, can be formally considered as the First Cause of Motion (in natural philosophy), the First Cause of Being (in metaphysics), and as the Supernatural Deity (in supernatural theology).