What does the Nicene Creed mean when it says that the Father and the Son are of the same substance? http://en.wikipedia.org/wiki/Nicene_Creed says:


  And in one Lord Jesus Christ, the Son of God, begotten of the Father
  [the only-begotten; that is, of the essence of the Father, God of
  God,] Light of Light, very God of very God, begotten, not made, being
  of one substance with the Father;


How are the Son and the Father different? In the Nicene Creed it seems that they are separate persons but sharing the same substance.

Do Catholics believe that there is a substance out of which God is made? What is the "substance" being discussed here?

We cannot say that Jesus is God in the sense of identity, because then Jesus is God and the Father is God so Jesus is the Father, which contradicts the doctrine.
The term the Nicene Creed uses for substance is homooúsios. This term was intentionally chosen to separate the Creed from various forms of Arianism that denied the divinity of Jesus. The Nicene Creed is arguing that Jesus is fully divine just like the Father. The common forms of nontrinitarianism at the time commonly denied the divinity of Christ by arguing that he was similar to the Father in attributes, similar in substance to the Father, or different in both attributes and substance. The Nicene Creed explicitly states the 'one in substance' to both affirm the divinity of Christ as well as affirm the truine Godhead. When communicating it in contemporary English, homooúsios is sometimes translated as 'of the same being.'

It is the foundational conception of the Trinity of all major forms of Christianity still in existence: Catholic, Orthodox, or Protestant. So no, it is not a distinctly Catholic belief. The substance in question is the 'divine being' of the Godhead: Father, Son, and Holy Spirit. Each is of the same substance in that they are all fully divine, inseparable yet distinct. It is through this concept of substance that Christians describe the Trinity as 'one God in three persons.' The three persons of the Trinity all share the same divine 'substance' in the sense that they constitute one God -- but they are each distinct from each other in their persons.