In Biblical times, special people such as Kings were anointed as a sign of their appointment. So we see that Jesus Christ was appointed for a special purpose.
Jesus quoted the prophet Isaiah to show he was "anointed" for a special work:
17 The book of the prophet Isaiah was handed to him. He opened the book, and found the place where it was written,
18 “The Spirit of the Lord is on me,
because he has anointed me to preach good news to the poor.
He has sent me to heal the broken hearted,
to proclaim release to the captives,
recovering of sight to the blind,
to deliver those who are crushed,
19 and to proclaim the acceptable year of the Lord.”
20 He closed the book, gave it back to the attendant, and sat down. The eyes of all in the synagogue were fastened on him. 21 He began to tell them, “Today, this Scripture has been fulfilled in your hearing.”
Tha Apostles Peter and John in a prayer of thansgiving after being released by the Jewish authorities mention that Jesus is God's "annointed":
27 “For truly, both Herod and Pontius Pilate, with the Gentiles and the people of Israel, were gathered together against your holy servant, Jesus, whom you anointed,
The Apostle Peter told his hearers that God anointed Jesus with the Holy Spirit:
38 even Jesus of Nazareth, how God anointed him with the Holy Spirit and with power, who went about doing good and healing all who were oppressed by the devil, for God was with him.
The Psalmist talks of a time of conflict between world leaders and God's anointed:
2 The kings of the earth take a stand,
and the rulers take counsel together,
against the LORD, and against his Anointed, saying,
3 “Let’s break their bonds apart,
and cast their cords from us.”