Question: "What is the anointing? What does it mean to be anointed?"
Answer: The origin of anointing was from a practice of shepherds. Lice and other insects would often get into the wool of sheep, and when they got near the sheep's head, they could burrow into the sheep's ears and kill the sheep. So, ancient shepherds poured oil on the sheep's head. This made the wool slippery, making it impossible for insects to get near the sheep's ears because the insects would slide off. From this, anointing became symbolic of blessing, protection, and empowerment.
The New Testament Greek words for “anoint” are chrio, which means “to smear or rub with oil” and, by implication, “to consecrate for office or religious service”; and aleipho, which means “to anoint.” In Bible times, people were anointed with oil to signify God’s blessing or call on that person’s life (Exodus 29:7; Exodus 40:9; 2 Kings 9:6; Ecclesiastes 9:8; James 5:14). A person was anointed for a special purpose—to be a king, to be a prophet, to be a builder, etc. There is nothing wrong with anointing a person with oil today. We just have to make sure that the purpose of anointing is in agreement with Scripture. Anointing should not be viewed as a "magic potion." The oil itself does not have any power. It is only God who can anoint a person for a specific purpose. If we use oil, it is only a symbol of what God is doing.
Another meaning for the word anointed is "chosen one." The Bible says that Jesus Christ was anointed by God with the Holy Spirit to spread the Good News and free those who have been held captive by sin (Luke 4:18-19; Acts 10:38). After Christ left the earth, He gave us the gift of the Holy Spirit (John 14:16). Now all Christians are anointed, chosen for a specific purpose in furthering God's Kingdom (1 John 2:20). "Now He who establishes us with you in Christ and has anointed us is God, who also has sealed us and given us the Spirit in our hearts as a guarantee" (2 Corinthians 1:21-22).