Jesus announced his calling and ministry as the Messiah with this verse. Additionally, we know that He is our great Prophet, Priest, and King. Raphael Patai explains the significance of being anointed and those who received it. I believe every righteous person who honored their anointing was privileged to stand as a witness pointing to the the Savior. Patai wrote:
Remarkably and characteristically, the term "Mashiah"—of which “Messiah” is the Anglicized form—had preceded the Messianic concept by many centuries. Originally, in Biblical usage, it simply meant “anointed,” and referred to Aaron and his sons, who were anointed with oil and thereby consecrated to the service of God (Exod. 28:41, etc.). The High Priest was termed “the Anointed [Mashiah] of God” (Lev. 4:3, 5, 16; 6:15). With the establishment of the monarchy, the same term was applied to the king: he was “the Anointed of the Lord” because he was installed in his high office by receiving the sacrament of anointment (1 Sam. 2:10, 35; 9:16; 24:7, etc.). A third type of divinely elected, the prophet, would also undergo the ceremony of anointing: Elijah, we read, was commanded by God to anoint Jehu as king over Israel, and Elisha the prophet in his own place (1 Kings 19:16).
(Patai, Raphael. 1979. The Messiah Texts. Detroit: Wayne State University Press., pgs xxi-xxii)