Anointing was a special ceremony among the Jews. It was sometimes used to express a special relationship or to elevate a guest in your home. This was the ordinary way in which anointing was used.

From a more official point of view, anointing was done to call attention to those who were chosen for one of the three major offices in the Jewish community. Prophets were sometimes anointed to their position with the title of messiahs (anointed one). See 1 Kings 19:16.

The high priest was also anointed to his office as seen in Exodus 29:29. At the beginning of the priesthood, all priests were anointed but afterwards only the high priest.

The Jewish kings were also anointed (1 Samuel 9:16; 10:1). This was done to set them apart and to show that they were recognized by God. In all these anointings olive oil was used. But, in Isaiah God anoints his people with the oil of gladness, the oil of joy.

Isa 61:3
To grant those who mourn in Zion,
Giving them a garland instead of ashes,
The oil of gladness instead of mourning,
The mantle of praise instead of a spirit of fainting.
So they will be called oaks of righteousness,
The planting of the Lord, that He may be glorified.

Jesus was God’s true anointed one. He was anointed by God rather than by man. This anointing set Jesus above the angels. This action was foreseen in the Psalms 45:6, 7 and is quoted by the Hebrew writer. Let me include this wonderful passage here.

Heb 1:8-9
But of the Son He says,

“YOUR THRONE, O GOD, IS FOREVER AND EVER,
AND THE RIGHTEOUS SCEPTER IS THE SCEPTER OF HIS KINGDOM.
“YOU HAVE LOVED RIGHTEOUSNESS AND HATED LAWLESSNESS;
THEREFORE GOD, YOUR GOD, HAS ANOINTED YOU
WITH THE OIL OF GLADNESS ABOVE YOUR COMPANIONS.”
NASU

Jesus was a prophet, high priest, and king. Anointed by God to serve the world in all three offices. Not an ordinary prophet or high priest or king. No, Jesus was anointed as The Prophet, The High Priest, and The King. No olive oil used here. He is anointed with the oil of joy and the oil of joy is spread to all who accept him as their prophet, high priest, and king. Following Jesus means a garland instead of ashes, gladness instead of mourning.