Here, in part, is what E.F.J. Payne, the pre-eminent Schopenhauer translator, said in his preface to "The World as Will and Representation about "Vorstellung
Its primary meaning is that of "placing before," and it is used by Schopenhauer to express what he himself describes as an "exceedingly complicated physiological process in the brain of an animal, the result of which is the consciousness of a [i]picture[/i] there." In the present translation "representation" has been selected as the best English word to convey the German meaning.... The word "idea" which is used by Haldane and Kemp in their English translation of this work clearly fails to bring out the meaning of [i]Vorstellung[/i] in the sense used by Schopenhauer.
This fits with his essentially Kantian division of the world into the noumenal "thing-in-itself" (the will) and the phenomenal (that which is perceivable by the senses as the representation of the will). As Schopenhauer stated: "no truth is more certain, more independent of all others, and less in need of proof than this, namely that everything that exists for knowledge, and hence the whole of this world, is only object in relation to the subject, perception of the perceiver, in a word, representation."