He is the image of the invisible God, the firstborn of all creation.
Paul articulately asserts the truth of the Incarnation in Colossians 1, but his use of "firstborn" does not mean that there was a time when the Son of God wasn't (any more than John 3:16's use of "begotten" does -- as the Nicene Creed insists, Jesus is "eternally begotten"). But Paul's use of "firstborn" here holds such a wealth of meaning: namely, as it applies to Christ's sovereign authority and to his redemptive activity.
Biblically and culturally speaking, the firstborn son carried the weight of the family inheritance on his shoulders. The family name rested first with him. In the absence of the father, he is the head of the family. The firstborn son receives more honor, more expectation, and more authority.
This is Jesus, of course. The author of Hebrews tells us he is the radiance of God's glory. Romans 8 tells us that he is the heir of God. Inheritance talk is big in Galatians and Ephesians and Titus and Hebrews.
As our older brother, Jesus is due the authority and the wealth he is owed.
But unlike all other older brothers -- and I am one, so I know -- he walks in a way worthy of his honor. For our sake!
All through the Scriptures, from the murderous Cain to the sniveling idiot brother of Jesus' parable of the Lost Son, the older brother is consistently an utter and absolute failure. (So are most of the younger brothers, actually, but God consistently chooses them to make a point, I think.)
But not Jesus. Where disobedience and disregard ruled the roost of the firstborn, Jesus obeys the Father perfectly, submits to the eternal cause of the glory of the Father completely, and cares for and rescues and sacrifices his own well-being for his younger siblings to the utmost.
Jesus is the older brother who will not trade his birthright for a bowl of soup. Jesus is the older brother who will not trade his siblings into slavery.
Jesus is the older brother who leaves the comfort of his Father's estate to seek out his lost brother among the brothels and pigsties and actually rescues him from the degradation of the mud and dresses him in the Father's robe of his own accord.
To borrow from Sinclair Ferguson, Jesus is the "true and better" older brother.
To borrow from a favorite line in a favorite movie, Jesus is the older brother who does his job. Everybody else is the other guy.