Plato's theory of forms was an attempt to explain all visible things as emanating from universal forms that were not matter but had some kind of substance.
http://en.wikipedia.org/wiki/Theory_of_Forms
These forms were unchanging and invisible. For example: all triangles had their existence because of a form called Triangle. Apparentaly the Triangle form was in all triangles.
Well, that's a cute llittle theory. It tries to explain how the universe came about. But Plato doesn't explain where the Forms came from or how they create specific individual objects in the universe.
The Aristotelian/Acquinas/Catholic tradition is completely different.
God can create anything he wants from nothing because He is Existence and is His own Existence.
There are no independently existing forms. There are forms created by God to make creatures what they are. The human soul is the form of the body without which the body as we know it could not be or do what it does and is. For example: imagine Shakespeare sitting at a computer keyboard writing a play about President Jimmy Carter. ( It would be a trajedy!
) We watch and see Shakespeare's body typing out the text of
The Trajedy of Jimmy Carter. 
Is the body of Shakespeare writing the book? Not really. The soul's intelligent puts together the play and tells the body to type it out. The soul makes Shakespeare Shakespeare rather than Genghis Khan. The soul is the form of the body.
Platonic Participation and Catholicism?
Linear Mode
