The Holy Spirit is a dominant theme throughout the book of Luke. The Holy Spirit fills individuals in Luke (John, Elizabeth, Mary, Jesus, Zechariah, Simeon, cf. 1:15, 1:35, 1:41, 1:67, 2:25, 3:22, etc), and the work of the Spirit is spoken of in contrast to the many “evil spirits” that cause damage to the individual (7:21, 8:2). The Spirit is associated in the births of both John and Jesus; John will be “filled with the Holy Spirit before birth” (1:15) and Jesus will be conceived through the power of the Holy Spirit (1:35). A common result from the infilling of the Holy Spirit is prophecy and praise (1:42-45, 1:64, 2:13). Joel Green and Scot Mcknight associate Luke’s use of the Spirit with prophetic acts that point to the recognition and assurance of salvation: “Elizabeth and Zechariah experience the Spirit of prophecy in invasive prophetic speech (the invasive quality denoted here by the Lukan favorite idiom “filled with” the Holy Spirit) … and as a result give oracles of recognition and assurance of salvation.”
The Holy Spirit appears in a very special way at Jesus’ water baptism (Lk 3:21-22; Mk 1:9-11; Mt 3:13-17; Jn 1:29-34).
It is interesting to note that in each of the Gospel accounts, Jesus’ baptism narrative introduces the rest of his ministry. What is really going on? What were the writers of the gospels telling their readers?
This moment is intentionally placed (in Luke’s account) in order to draw attention away from John the Baptism and centre in on Jesus. What Luke is saying to his readers, is that something special is going on here, a prophetic act in which the New Covenant is being announced. It’s like he’s saying “It’s time for the project of the New Creation to begin, and it begins here, with Jesus.”
Scholars don’t agree on the purpose of the dove ascending on Jesus, and what that may intend to mean. I believe that it’s meant to allude to 1) the Noah narrative, where the dove was a messenger of new beginnings (Gen. 8:8-12), and 2) the creation narrative, where God’s Spirit hovers over the waters right as he is about to bring forth creation ex nihilo (Gen. 1:2). The point, I think, is that God is now doing something NEW in Jesus. The project of New Creation is beginning in Jesus who is the Christ.
8 “The Spirit of the Lord is upon me,
because he has anointed me
to proclaim good news to the poor.
He has sent me to proclaim liberty to the captives
and recovering of sight to the blind,
to set at liberty those who are oppressed,
19 to proclaim the year of the Lord’s favor.”
 Dictionary of Jesus and the Gospels, ed. Joel B. Green and Scot Mcknight (Downers Grove, IL: InterVarsity Press, 1992), 342.