"Since many have undertaken to compile a narrative of the events that have been fulfilled among us, 2 just as those who were eyewitnesses from the beginning and ministers of the word have handed them down to us, 3 I too have decided, after investigating everything accurately anew, to write it down in an orderly sequence for you, most excellent Theophilus, 4 so that you may realize the certainty of the teachings you have received.
14 Jesus returned to Galilee in the power of the Spirit, and news of him spread throughout the whole region. 15 He taught in their synagogues and was praised by all. 16 He came to Nazareth, where he had grown up, and went according to his custom into the synagogue on the Sabbath day. He stood up to read 17 and was handed a scroll and found the passage where it was written:
18 The Spirit of the Lord is upon me, because he has anointed me to bring glad tidings to the poor. He has sent me to proclaim Liberty to the captives and recovery of the sight to the blind. To let the oppressed go free, 19 and to proclaim a year acceptable to the Lord.
20 Rolling up the scroll, he handed it back to the attendant and sat down, and the eyes of all in the synagogue looked intently at him. 21 He said to them, "Today this scripture passage is fulfilled in your hearing."
It is interesting to note that St. Luke wrote his Gospel starting with a literary prologue. He is the only evangelist among the synoptic gospel writers to do so. St. Luke clearly wasn't one of the disciples of Jesus; he was probably a second or a third generation Christian, hence when he wrote the Prologue he practically pointed out that "those who were eyewitnesses from the beginning and ministers of the word have handed them down to us." He was writing his Gospel based on what he heard or perhaps read from those who were eyewitnesses to the events in the life of Jesus, many of which were already written in those days long before the Bible was even compiled.
This tells us a lot about the beginnings of Christianity... that the early Christians only heard the word from the apostles or disciples of Jesus and no doubt, this included the many sick, lame or possessed people whom Jesus had healed. Not to mention how he raised Lazarus from the grave. For instance, if you were one among the five thousand who heard Jesus preach in the Sermon of the Mount, surely you must have eaten the miraculous fish and bread that came from a basket of five loaves of bread and two fishes.
Indeed, there were thousands of eyewitness accounts about the man from Nazareth whom many would say was truly the Son of God. They were all over Palestine, from Capernaum, Sidon, Tyre to Galilee down to the Jordan River and yes Jerusalem. Surely as St. Luke pointed out, many of them wrote about their eyewitness experiences with Jesus the Nazorean. Since a lot of these things were written down, St. Luke probably thought that some of those stories were not written in proper order or were watered down stories of the real events. Hence he took it upon himself to write them in its proper sequence as he pointed out to his friend Theophilus.
The second part of Luke's Gospel, on 4:14-21, he wrote that by that time, Jesus had already gain an immense following as he was already teaching in many synagogues when he came back to the place where he grew, in Nazareth. Why was this event significant to Christianity? Firstly, it is because it was the first time that our Lord Jesus truly revealed to the Jews that he was really the man or the messiah that the whole Jewish nation has been waiting for in a long time.
Let me quote that particular passage, "The Spirit of the Lord is upon me because he has anointed me to bring glad tidings to the poor. He was referring to himself as the Lord's anointed one, especially when he announced to everyone listening in the synagogue, "Today this scripture passage is fulfilled in your hearing." Everyone in Nazareth was amazed at holiness of Jesus to the point of disbelief when they asked, "Isn't he the son of Joseph?
But the people of Nazareth rejected Jesus for claiming that he was actually the Messiah, which is why he said, "No prophet is accepted in his own native place." His own townsfolk then drove him out of the synagogue. This was indeed a very prophetic event as the Nazoreans rejected their own, Israel too rejected the long awaited Messiah. In the end, Christianity blossomed everywhere to Gentiles all over the world. While the Jews today continue to await their Messiah who had already come to them 2,000 years ago.