We learn in Luke that John the Baptist's father was a priest and therefore a Levite. Why does this matter? Luke captures the Davidic aspect of Christ by highlighting the fact that Christ was baptized (i.e. anointed) by a Levite.
King David and all of his successors were anointed King and Messiah by Levites. John the Baptist does the honor for Christ who is the Davidic King of all Israel. Christ is anointed by the Father with the Holy Spirit through the instrumental action of the Levite John the Baptist.
This transferal from a Levite to a Judahite is the transferal of the Old Covenant to the New Covenant.