1 Peter 1:13-21 (NKJV) is captioned "Living before God our Father". These verses outline some of God's expectations of us believers whom He has begotten through the "resurrection of Jesus Christ from the dead". Verses 15-16 is a call to to holiness, "... but as He who called you is holy, you also be holy in all your conduct, because it is written, “Be holy, for I am holy.” I Peter 1:15-16. Here, the Apostle Peter quoted Leviticus 11:44 to let them know the call to holiness is not new. Peter starts this chapter by telling us who we are in Christ and then sets forth the basic imperatives of Christian living. One of these is holiness.
Holiness usually conjures a list of dos and don'ts, but it more than that. The reason why God is asking us to be holy in this verse is simply that He who has chosen us is holy. He is different, He is set apart from all else, there is no trace of sin in Him. God is not asking us to strive by our own strength to be holy. "I have been crucified with Christ; it is no longer I who live, but Christ lives in me;... says Paul in Galatians 2:20. He says again in Colossians 3:3 that our lives are "hidden with Christ in God.".
Since we are no longer chained to the old life/self but united in and with Christ, by virtue of this union, we can participate in God's holiness. Holiness then is a consequence of our being called into God's family. It is one of the ways in which we show the world that we belong to Christ.
In understanding what Peter meant by being holy in verse 16, we must look at verse 14 which precedes this command. It says "as obedient children, not conforming yourselves to the former lusts, as in your ignorance".
Once we come to Christ we are expected to live differently than we did in the past. Our desires change, we develop a thirst for the things of God and we long to please Him with our conduct. We are able to do this with the help of the Holy Spirit. The more we yield to Him, the more He makes us like Christ.
By asking us to be holy, Peter is saying that as believers we need to be set apart from the world; we must live by God's standards and not the world's. In 1 Peter 2:9, he calls us "a holy nation"; we are in the world but not of the world and our every conduct must reflect that. Blending in is not an option, conforming to the world and doing everything unbelievers do is not what we are about. May God grant us the grace to be holy as He is holy and help us avoid and resist the temptation to sin.