The call to pursue holiness is the call to obedience as we are sanctified by the power of the Holy Spirit. The English word "sanctification" in the New Testament is a translation of the Greek word ἁγιασμός, which comes from the root word άγιος, denoting holiness. In other words, to be sanctified is to be made holy! Therefore, understanding the process of sanctification begins with understanding holiness. Defining holiness can be difficult, as it is a term that may be interpreted in various ways. In fact, the Westminster Dictionary vaguely defines it as a "peculiar quality of the religious."
For the Christian seeking to define holiness from Scripture, I would define it as everything that pertains to who God is. This is why Peter says we are called to be holy as God is holy, quoting from Leviticus (1 Peter 1:16). The aim of growing in holiness is to become a progressively clearer reflection of who God is.
In Colossians 3, Paul contrasts what he refers to as the "earthly nature," or the old self, with the new self. Paul says that this new self is being renewed in the image of its Creator. The language he uses indicates that, in our sanctification, we are being renewed into the image of Christ. Here, we find an excellent definition of holiness: "renewed in knowledge after the image of its Creator" (Colossians 3:10). To be made holy is the process of being transformed into the image of the triune God. There is no true definition of holiness apart from God—only in God Himself does the term find meaning.
Jesus Christ is the full revelation of God in the flesh; therefore, the way we are made holy is by following Him in obedience. In following Christ, we grow in holiness as we are conformed by the work of the Spirit into the image of Christ. This means, first and foremost, that we increasingly share in the character of Christ—holiness is having Christlike character. Being like Christ means we share His attitudes and actions.
Take a moment to think through some of the attitudes and actions mentioned by Paul in his command to the church in Colossae. They were called to put to death sexual immorality, impurity, lust, evil desires, greed, anger, rage, malice, and filthy language (Colossians 3:5-8). These things are incompatible with the character of Christ and, therefore, with anyone claiming to be a follower of Christ. Holiness is not only the absence of such things—for it not only puts to death what is contrary to Christ’s character, but it also puts on what is consistent with His character: compassion, kindness, humility, meekness, patience, forgiveness, forbearance, love, and gratitude (Colossians 3:12-16).