“What does Paul mean when he says that he was the minister of Jesus Christ to the Gentiles ‘that the offering up of the Gentiles might be acceptable, being sanctified by the Holy Ghost (Rom. 15:16)?”
Under the Law, the Gentiles couldn’t offer themselves up as an offering that would be “acceptable” unto God as Paul tells us to do (Rom. 12:1,2). But now we are “sanctified” or set apart to God by the Holy Spirit–that is, by the Word of the Spirit, the words the Spirit teaches in His Word (1 Cor. 2:13). In His rightly divided Word, He teaches in Paul’s epistles that the grace of God is now available to Gentiles as well as to Jews. Paul told the Ephesian elders,
“…the word of His grace…is able to build you up, and to give you an inheritance among all them which are sanctified” (Acts 20:32).
See the connection? The Jews were sanctified, and so their sacrifices were acceptable to God, and now we too are sanctified by “the word of His grace” that the Spirit presents in His Word through the Apostle Paul.
So when the Macedonians “gave their own selves to the Lord,” they were able to do this “by the will of God” (2 Cor. 8:5). They couldn’t have done that under the Law, for God wouldn’t have accepted their offering. But under grace, “the offering up of the Gentiles” is “acceptable, being sanctified by the Holy Ghost.” source