Witness Lee defines it like this,
The record in the Gospel of Luke has a particular characteristic. This characteristic is that Luke always shows us in the Man-Savior the mingling of the divine attributes with the human virtues to produce the highest standard of morality for the New Testament jubilee.
The beauty and loveliness of Luke’s Gospel lies in the stories and sayings he records, which vividly capture the interaction between Jesus’ human and divine natures. This interaction produces a unique kind of morality, a quality of conduct that is supremely right and good. When a human being comes into contact with that species of conduct, he or she experiences a liberating salvation.
The following quote from A. T. Robertson sums up well some general thoughts I am keeping in mind as I read. It particularly touches on, what can be called, the principle of incarnation by highlighting aspects of Luke’s person.
According to this principle, what the Lord wants to reveal and impart, He does through a human channel. However, the human vessel needs to match the content of the ministry that flows through him. In this way there is no separation between what one is and what one does. Otherwise, we may build up some by what we do, but tear down more by what we are. The most important thing in the work is the person.
So, here is Luke…
He was the most versatile of the Gospel writers. He was a Greek, a Christian, a physician, a man of travel, a man of world-outlook, sympathetic, cultured, poetic, spiritual, artistic, high-minded… The breadth of his literary equipment is thereby shown. He not only uses many medical terms common to technical circles, but he has the physician’s interest in the sick and afflicted, as shown in the large number of miracles of healing narrated. His interest in the poor is not due to Ebionitic prejudice against the rich, but to human compassion for the distressed. His emphasis on the human side of the work of Jesus is not due to Ebionitic denial of the Divinity of Jesus, but to his keen appreciation of the richness of the human life of the Son of God.
His rich and varied vocabulary reveals a man who read and mingled with the best life of his time. He wrote his books in the vernacular, but the elevated vernacular of an educated man touched with a distinct literary flavor. His poetic temperament is shown in the preservation of the beautiful hymns of the nativity and in the wonderful parables of Jesus in chapters 10, 15-18. They are reported with rare grace and skill. Luke is fond of showing Christ’s sympathy with women and children, and he has more to say about prayer than the authors of the other Gospels.
His cosmopolitan sympathies are natural in view of his training and inheritance, but part of it is doubtless due to his association with the apostle Paul. He comes to the interpretation of Jesus from a world-standpoint and does not have to overcome the Pharisaic limitations incident to one reared in Palestine. It is a matter of rejoicing that we have this book, called by Renan the most beautiful book in the world, as a cultured Greek’s interpretation of the origin of Christianity. He thus stands outside of the pale of Judaism and can see more clearly the world-relations and world-destiny of the new movement.
With Luke, Jesus is distinctly the world’s Saviour. The accent on sin is human sin, not specifically Jewish sin. John in his Gospel came in his old age to look back upon the events in Judea from a non-Jewish standpoint. But he rose to the essentially spiritual and eternal apprehension of Christ, rather than extended his vision, as Luke did, to the cosmopolitan mission and message of Jesus, though this did not escape John. The Gospel of Luke thus has points of affinity with Paul, John and the author of Hebrews in style and general standpoint. But while Luke’s own style is manifest throughout, it is not obtrusive. He hides himself behind the wonderful portrait of Jesus which he has here drawn in undying colors.
(International Standard Bible Encyclopedia, “Gospel of Luke”)