Sanctification refers to being set apart as holy and to the process of living in increasing conformity to God's holiness.
Easton’s Bible Dictionary (1897)
Involves more than a mere moral reformation of character, brought about by the power of the truth: it is the work of the Holy Spirit bringing the whole nature more and more under the influences of the new gracious principles implanted in the soul in regeneration. In other words, sanctification is the carrying on to perfection the work begun in regeneration, and it extends to the whole man (Rom. 6:13; 2 Cor. 4:6; Col. 3:10; 1 John 4:7; 1 Cor. 6:19). It is the special office of the Holy Spirit in the plan of redemption to carry on this work (1 Cor. 6:11; 2 Thess. 2:13). Faith is instrumental in securing sanctification, inasmuch as it (1) secures union to Christ (Gal. 2:20), and (2) brings the believer into living contact with the truth, whereby he is led to yield obedience "to the commands, trembling at the threatenings, and embracing the promises of God for this life and that which is to come." Perfect sanctification is not attainable in this life (1 Kings 8:46; Prov. 20:9; Eccl. 7:20; James 3:2; 1 John 1:8). See Paul's account of himself in Rom. 7:14-25; Phil. 3:12-14; and 1 Tim. 1:15; also the confessions of David (Ps. 19:12, 13; 51), of Moses (90:8), of Job (42:5, 6), and of Daniel (9:3-20). "The more holy a man is, the more humble, self-renouncing, self-abhorring, and the more sensitive to every sin he becomes, and the more closely he clings to Christ. The moral imperfections which cling to him he feels to be sins, which he laments and strives to overcome. Believers find that their life is a constant warfare, and they need to take the kingdom of heaven by storm, and watch while they pray. They are always subject to the constant chastisement of their Father's loving hand, which can only be designed to correct their imperfections and to confirm their graces. And it has been notoriously the fact that the best Christians have been those who have been the least prone to claim the attainment of perfection for themselves.", Hodge's Outlines.
Sources: Easton’s Bible Dictionary (1897)
A Biblical and Theological Dictionary
that work of God’s grace by which we are renewed after the image of God, set apart for his service, and enabled to die unto sin and live unto righteousness. Sanctification is either of nature, whereby we are renewed after the image of God, in knowledge, righteousness, and true holiness, Eph. iv, 24; Col. iii, 19, or of practice, whereby we die unto sin, have its power destroyed in us, cease from the love and practice of it, hate it as abominable, and live unto righteousness, loving and studying good works, Tit. ii, 11, 12. Sanctification comprehends all the graces of knowledge, faith, repentance, love, humility, zeal, patience, &c, and the exercise of them in our conduct toward God or man, Gal. v, 22–24; 1 Peter i, 15, 16; Matt. v, vi, vii. Sanctification in this world must be complete; the whole nature must be sanctified, all sin must be utterly abolished, or the soul can never be admitted into the glorious presence of God, Heb. xii, 14; 1 Peter i, 15; Rev. xxi, 27; yet the saints, while here, are in a state of spiritual warfare with Satan and his temptations, with the world and its influence, 2 Cor. ii, 11; Gal. v, 17, 24; Rom. vii, 23; 1 John ii, 15, 16.
Sources: A Biblical and Theological Dictionary