What does Tertullian mean by the Son being a "portion of the Father's substance"? What does Tertullian mean by the Son being a "portion of the Father's substance"? 


  "For the Father is the entire substance, but the Son is a derivation
  and portion of the whole" (Against Praxeas, Chapter 9).


Tetullian seemed to contradict the Scriptures:


  For the entire fullness of God's nature dwells bodily in Christ, 
  
  Colossians 2:9 (HCSB)


If not, what does he mean by the Son being a derivation and portion of the whole substance?
This phrase is commonly seen to indicate Tertullian's belief in ontological subordinationism, that is, that God the Son is subordinate to God the Father in both his nature and role.  Views like this were later declared heretical at the Council of Nicaea; now, only a relational or functional subordinationism, in which Jesus is subordinate in role only, is normally considered orthodox.

Tertullian's concept of Jesus being a "portion" of God is perhaps best seen in the analogies he used to argue that God and Jesus had a common substance:


  For God sent forth the Word, as the Paraclete also declares, just as the root puts forth the tree, and the fountain the river, and the sun the ray. For these are προβολαί, or emanations, of the substances from which they proceed. I should not hesitate, indeed, to call the tree the son or offspring of the root, and the river of the fountain, and the ray of the sun; because every original source is a parent, and everything which issues from the origin is an offspring. (Against Praxeas, 8)


From an orthodox trinitarian perspective, however, this is problematic, because it only affirms that Jesus and God have a common nature, like a human son has the same "nature" as his father.  This is likely the sense in which he would understand Colossians 2:9, but it's very different from the "numerical unity of essence" understanding of trinitarianism.   Alvan Lamson extensively quotes from Tertullian's writings to show that "he regarded the Son as inferior," and concludes:


  We might multiply our quotations without number, but it is unnecessary.  Judged according to any received explanation of the Trinity at the present day, the attempt to save Tertullian from condemnation would be hopeless. (The Church of the First Three Centuries, 106–9)


Ontological subordinationism is also associated with Origen, but the challenge of Arianism led the church to look at these views more critically.  Placher and Nelson explain:


  The difficulties of [Tertullian's subordinationism] became clear only in the theories of Arius, a priest living in Alexandria around 300, whom tradition has cast as the villain of this story.  Arius wanted to make it absolutely clear that the Son is not identical with the Father. (A History of Christian Theology, 60)


Ultimately Arianism, and, by extension, ontological subordinationism, was rejected as heresy in the Council of Nicaea.  The fact that Tertullian died before that Council is usually considered a point in his favor, since he never had the opportunity to submit himself to the Church on this point.  But these views, along with his association with another heretical movement, Montanism, have diminished his status as an orthodox theologian in Nicene Christianity.