Concise Bible Dictionary:
This term occurs only in 1 John 2:20, though the same word, χρίδμα, is twice translated “anointing” in 1 John 2:27. The Holy Spirit is an unction that permeates, as it were, the whole being of the Christian to give him Christ's character.
From Anstey’s Doctrinal Definitions:
This is an aspect of the Holy Spirit’s indwelling that emphasizes the Spirit’s work in the believer to give him the powers of discernment in connection with truth and error (1 John 2:20, 27). If the believer walks in the Spirit in communion with the Lord, he will have the power to discern what is the truth and what is error when he is confronted with either (1 John 4:6). The Apostle John said, “The anointing [unction] which ye have received of Him abideth with you, and ye need not that any man teach you: but as the same anointing teacheth you of all things, and is truth, and is no lie, and even as it hath taught you, ye shall abide in Him” (1 John 2:27). Some have used this verse to refuse teaching from gifted teachers because they have the Holy Spirit and they think that that all they need. Consequently, they will not read any books of ministry, etc. But that is not what this verse is saying. The Apostle John is not saying that all believers instinctively know the truth because they have the Spirit. If that were true, why has God given “teachers” to the Church? (1 Cor. 12:28; Eph. 4:11) The verse simply means that when truth or when error are presented to us, we do not need someone to tell us that it is such. If we are in communion, and thus “abide in Him,” the “unction” of the Spirit in us will give us to know whether it is the truth or not.