To sanctify means to be set apart for a holy use. God has set us apart for the purpose of sanctification, not impurity (1 Thess. 4:7), and being such we are called to do good works (Eph. 2:10).
Christians are to sanctify Christ as Lord in their hearts (1 Pet. 3:15). God sanctified Israel as His own special nation (Ezek. 27:28). People can be sanctified (Exodus 19:10, 14) and so can a mountain (Exodus 19:23) as can the Sabbath day (Gen. 2:3), and every created thing is sanctified through the word of God and prayer (1 Tim. 4:4-5).
Sanctification follows justification. In justification, our sins are completely forgiven in Christ. Sanctification is the process by which the Holy Spirit makes us more like Christ in all that we do, think, and desire. True sanctification is impossible apart from the atoning work of Christ on the cross because only after our sins are forgiven can we begin to lead a holy life.