The Priests of God were anointed with the holy anointing oil, which represented the scent of the Lord. Being thus anointed, the priests were a type of representation of the Lord.
When that Priest anointed another human they consecrated or made sacred; dedicated to God, often in a ceremony that includes dabbing or sprinkling with holy oil:
Anointing someone with oil signifies that they have been chosen by God and are unique to him. It is also a way of signifying that the Holy Spirit has empowered them for their specific role or purpose.
The anointing—the oil of Scripture—is directly related to the Holy Spirit's work in our life (2 Cor. 1:21-22).
This was done to Saul, symbolizes he was "SAVED" and he later rejected God.