Jesus described the anointing in Luke 4:18-19:
“The Spirit of the LORD is upon Me,
Because He has anointed Me
To preach the gospel to the poor;
He has sent Me to heal the brokenhearted,
To proclaim liberty to the captives
And recovery of sight to the blind,
To set at liberty those who are oppressed;
To proclaim the acceptable year of the LORD.”
John the Baptist describes the anointing of the Holy Spirit on Jesus with two comments. First, he described seeing the Holy Spirit coming and resting on Him, then he explains the magnitude of Christ’s anointing: “For He whom God has sent speaks the words of God, for God does not give the Spirit by measure.” John 3:34. So there is a definite point when the anointing comes on a servant of God, and any limits on what God can do through someone He anoints are not because of limits in the Holy Spirit.
In the Book of Acts the anointing is indicated with the phrase “filled with the Holy Spirit”, in situations where the anointed men spoke the word of God, like Peter, the church with Peter, and Paul. Luke uses the same phrase to describe Jesus at the beginning of His preparation for public ministry. Jesus commanded reliance on the anointing of the Holy Spirit for speaking His words in dire situations in Mark and Luke.
So the anointing is power from God for supernatural good works through an infilling by the Holy Spirit. Is that simple enough? Probably not, because what we really want to know is how to tell when someone, including each of us, is anointed. The goal is to keep from being deceived, which often happens when there is an “anointed one”. How can we tell? What happens when someone is anointed? What are the true signs of anointing?