What does the phrase "God of God" means in the Nicene Creed? What does the phrase "God of God" means in the Nicene Creed? 


  We believe in one God, the Father Almighty, Maker of all things
  visible and invisible. 
  
  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; 
  
  By whom all things were made both in heaven and on earth; 
  
  Who for us men, and for our salvation, came down and was incarnate and
  was made man; 
  
  He suffered, and the third day he rose again, ascended into heaven; 
  
  From thence he shall come to judge the quick and the dead. 
  
  And in the Holy Ghost. 
  
  But those who say: 'There was a time when he was not;' and 'He was not
  before he was made;' and 'He was made out of nothing,' or 'He is of
  another substance' or 'essence,' or 'The Son of God is created,' or
  'changeable,' or 'alterable'—they are condemned by the holy catholic
  and apostolic Church.


Reference: 

http://www.churchhistory101.com/century4-p8.php
The phrase “God of God” means that a person came from a person ( like an offspring from a parent) and that they are of same nature. It is analogous to the phrase “Human of Human,” That is, a human offspring of a human parent.


  To beget is to produce someone to have one’s nature.


Seth is begotten of Adam. Seth and Adam are of same nature.
A human person from a human person. Therefore, Human of Human.

The Son is begotten from the Father. The Father and the Son are of same nature.A divine person from a divine person. Therefore, God of God

The phrase “God of God” originated from John 1:1.In this text, it is said that the self-knowledge and self-expression of God is “God.” That is, “the thought ( of God about himself) was God” or simply put, “the Word was God” as majority of English translation reads.Θεος in John 1:1c as well as in John 1:18a is anarthrous yet it is translated into English as a proper noun: “God.”


  John 1:1 (ESV)
  
  In the beginning was the Word, and the Word was with
  God, and the Word was God.


The disciple John didn't write John 1:1 in vacuum. He had Jewish ideas which helped him out to write it. In his day, the concept of the λόγος was very well known because of first century Hellenistic Judaism in the Second Temple Judaism. This is evident in the Septuagint as well as in religious Jewish writings in the inter-testamental period. Due to its popularity, John took advantage of this concept to spread the Good News. Genesis 1:1 (LXX), Psalm 45:1 (LXX), 33:6 (LXX) and Proverbs 8:22-30 (LXX) are the foundational biblical basis of John 1:1-3.

The Greek word λόγος has many meanings like speech, word, message, plan and reason. It depends on the context of the text as to what meaning it takes.

Thought and word. These definitions are what John had in his mind when he wrote John 1:1. Both definitions entails 'reasoning' ( thinking from the mind).In fact, it can simply be defined as “expression from the inside out.”

In John 1:1, the λόγος is the self-thought of God. The reason is that God alone existed before creation and is the only one present in the beginning of creation ( John 1:1-3). John 1:1 underscores God in relation to Himself. God knows in his mind that he is 'God.' KAITHEOSENOLOGOS( and God was the thought). Before anything else come into existence, only God exists and yet he was not alone for he has with Him his λόγος (self-thought, self-knowledge, self-expression).

Thinker = God

Thought = God

This is clearly the “God of God” in the Nicene Creed. It is a faithful preservation of the biblical truth in a creedal statement.

The self-knowledge of God is towards God [himself] and hence, self-expression (i.e. The Word).The Word or self-expression (from self-knowledge) is "God." God does not think that he is partly God.Rather, God thinks that he is 'God' in all his fullness.


  Proverbs 23:7 (KJV)
  
  For as he thinketh in his heart, so is he.


According to John 1:1, the Word of God is “God of God.”

References

http://biblehub.com/john/1-1.htm

http://www.newadvent.org/fathers/2821.htm

http://www.tektonics.org/guest/psnicea.html