Luke 4:14-15 meaning

The parallel gospel accounts for this passage are Matthew 4:17 and Mark 1:14-15.

And Jesus returned to Galilee in the power of the Spirit, and news about Him spread through all the surrounding district (v 14).

After the events of Luke 3 and the temptation of Jesus in Luke 4:1-13, Jesus returned to the district of Galilee. 

The reason Luke refers to Galilee as a district is because that is how most of his Gentile audience would have known about it. Most of the Greeks he wrote to would likely not have visited or lived here. They would not necessarily understand its (largely Jewish) history, but they would have known about it as a district within the Roman province of Judea.

Galilee was a Roman district that was located on the western half of the Sea of Galilee. It was north and east of the district of Samaria and south and east of the district of Phoenicia. To its northwest was the district of Gaulanitis and to its southwest was the Roman Decapolis. The district of Galilee served as an Imperial toll booth because two major highways converged within it connecting Egypt with Rome in the West and Persia to the East. 

The reason Luke writes that Jesus returned to Galilee was because Galilee was the district in which He was raised and spent the years of His early adulthood. The town of Nazareth, where Jesus was raised (Matthew 2:22-23) and would soon visit (Luke 4:16), was located in the southwestern portion of the district. 

Capernaum, a small fishing village on the northern shoreline by the Sea of Galilee, is where Jesus would soon headquarter His ministry (Matthew 4:13; Luke 4:31). 

Jesus began His public ministry in Galilee, away from an unbelieving Jerusalem. 

Matthew expressed Jesus's arrival in Galilee to his Jewish audience by pointing out how Jesus's ministry in Galilee was a direct fulfillment of a Jewish prophecy (Isaiah 9:1-2) which demonstrated how Jesus was the Messianic King the Jews were waiting for. 

Luke does not point this prophetic fulfillment out to his Greek audience, probably because it would not have meant as much to them. Instead, Luke describes Jesus's return to Galilee according to one of His book's themes—the power of the Spirit.

The Gentile believers for whom Luke was writing, were familiar with the power of the Holy Spirit because they had heard, witnessed, and/or experienced the Spirit's impact as the Christian faith spread throughout the Roman Empire. Remember, Luke is author of both Acts and this Gospel, and he emphasizes the presence and role of the Holy Spirit in both works. During the time of Jesus's earthly life, the Holy Spirit had not yet come to God's people. He (the Holy Spirit) first came to apostles about ten days after Jesus ascended into heaven (Acts 2:1-4) as Jesus predicted (Luke 11:13, 12:12; John 14:16-17). 

By explaining the Spirit's role throughout Jesus's life, whether it was His conception (Luke 1:35), His baptism (Luke 3:21-22), His time in the wilderness (Luke 4:1-2), or in this passage at the beginning of His public ministry, Luke is connecting the lived faith and power from the person of the Holy Spirit that the believers in his generation experience with the same lived faith and power from the person of the Holy Spirit that Jesus knew. The same Spirit that guided and empowered Jesus is the same Spirit that guides and empowers the lives of believers. In Jesus we have the perfect example for how to live the good life (which was so important to the Greeks). The good life is attained as Jesus attained it, by following and relying upon God's Spirit. 

Luke also reveals in this verse the mystery of the Trinity and the founding paradox of reality—the paradox of God. God is Three and God is One. God is God and in the person of Jesus, God is human. Jesus Christ is the God-man. 

See the Bible's Says article: "Founding Paradox" to learn more about this paradox.

Even though Jesus is God, He also listens to and heeds the Spirit's guidance perfectly. If Jesus, who is God, listened to and heeded the Spirit, how much more should we, who are not God, listen to the Spirit's guidance for our lives?

In John's Gospel, Jesus repeatedly confesses that His purpose is to do His Father's will; that He does nothing of His own volition; that He only speaks what His Father tells Him. In following the Holy Spirit, Jesus is repeating a similar pattern. Luke's Gospel emphasizes God-the-Son's reliance upon God-the-Spirit as John's Gospel emphasizes God-the-Son's reliance upon God-the-Father (John 1:14, 1:18, 5:19, 5:36, 8:28, 8:38, 12:49-50, 14:10, 14:23, 15:1, 16:28, 16:32, 18:11, 20:21). 

As we saw in Luke 3:21-22, Jesus was commissioned by the Spirit and the Father to begin His ministry as Savior of the world. Jesus begins by demonstrating exactly how a person ought to live: surrendered, yielded, and obedient to the Holy Spirit. Living a life in this posture of submission to the Holy Spirit results in walking in the power of the Spirit. The Apostle Paul speaks to this relationship and the power of the Spirit throughout his epistles in the New Testament:

"For I will not presume to speak of anything except what Christ has accomplished through me, resulting in the obedience of the Gentiles by word and deed, in the power of signs and wonders, in the power of the Spirit; so that from Jerusalem and round about as far as Illyricum I have fully preached the gospel of Christ."
(Romans 15:18-19)

"And my message and my preaching were not in persuasive words of wisdom, but in demonstration of the Spirit and of power, so that your faith would not rest on the wisdom of men, but on the power of God."
(1 Corinthians 2:4-5)

"For our gospel did not come to you in word only, but also in power and in the Holy Spirit and with full conviction; just as you know what kind of men we proved to be among you for your sake."
(1 Thessalonians 1:5)

Jesus was the perfect embodiment of a man living in submission to God and living out the power of the Spirit. This would have connected with Luke's audience of Greek Gentiles who were concerned about the notion of the ideal man and who were looking for a better way to live (1 Corinthians 1:22b). 

Because Jesus was living in this manner and the Spirit's power was evident in Him, news about Him spread through all the surrounding district of Galilee. 

And He began teaching in their synagogues and was praised by all (v 15).

Synagogues were community centers where Jews gathered to worship God and listen to teachings from rabbis who interpreted God's word. The synagogues were the domain of the religious party called the Pharisees. The Pharisees viewed themselves and were largely seen by the people as champions of righteousness and the protectors of Jewish law. But in reality, the righteousness of the Pharisees was fake. Instead of serving people, they manufactured an ever-multiplying web of laws designed to exploit others and make themselves look good (Matthew 23). 

At this point Jesus was a new rabbi. Rabbis were teachers of the law and had followers. In order for Jesus to be able to teach in a synagogue He had to be invited to do so by the head of the synagogue. We know from Luke 2:41-52 that even as a young boy Jesus possessed amazing knowledge and insight into the scriptures. As a thirty-year-old man, Jesus would have grown even further in wisdom and knowledge. The ruins of ancient synagogues are observable among the ruins of ancient Capernaum as well as the nearby ruins of villages identified as Chorazin, and Magdala. (See image.)

From verse 14 we know that the news about Him spread through all the surrounding district. 

Matthew also tells us what the main message of Jesus's ministry concerned,

"From that time Jesus began to preach and say, 'Repent for the kingdom of heaven is at hand.'"
(Matthew 4:17)

The message of Jesus was similar to the message of Jesus's cousin, who was His forerunner—John the Baptist (Matthew 3:2; Luke 3:3). The message of that the long-awaited Messianic kingdom was at hand resonated in the hearts of the Jewish inhabitants through all the surrounding district. This kingdom is prophetically promised and described in 2 Samuel 7:12-13, Psalm 118:24-26, Isaiah 25:6-10, 26:1-21, Daniel 9:13-14) Partnership in the Messianic kingdom is available to Gentiles (Isaiah 27:13, 49:1, 49:6-7, 52:15; Matthew 8:5-12; Ephesians 3:6; 2 Peter 1:1-11). 

Luke tells His readers elsewhere how Jesus proclaimed this same kingdom (Luke 8:1).

The fact that Jesus was praised by all for His teaching seems to explain how the news about Him travelled throughout the district of Galilee. A new teacher "accurately handling the word of truth" (2 Timothy 2:15) and preaching in the power of the Spirit, proclaiming the good news of the kingdom (Matthew 4:17) should illicit such a positive response from God's people.