You shall be holy

Peter was writing to the Jewish Diaspora in Pontus, Galatia, Cappadocia, Asia, and Bithynia (1 Peter 1:1). Therefore, we expect the intended readers to be familiar with the Hebrew Scripture. Unlike Matthew, who wrote that
You, therefore, must be perfect τέλειοι , as your heavenly Father is perfect τέλειός (Matthew 5:48).
Peter quoted Leviticus and wrote instead
You shall be holy (Hebrew קְדֹשִׁים) ἅγιοι, for I am holy (Hebrew קָדוֹש)  ἅγιός (1 Peter 1:16)
The intended readers are supposed to understand what Peter refers to. Though we are not Jews, we have also inherited the Hebrew scriptures. So, let's find out what Peter intended to say.
The quotation comes from Leviticus. There are three occurrences.
For I am the LORD your God; consecrate yourselves therefore, and be holy, for I am holy. You shall not defile yourselves with any swarming thing that crawls upon the earth.
For I am the LORD who brought you up out of the land of Egypt, to be your God; you shall therefore be holy, for I am holy (Leviticus 11:44-45).
Say to all the congregation of the people of Israel, You shall be holy; for I the LORD your God am holy (Leviticus 19:2).
You shall be holy to me; for I the LORD am holy, and have separated you from the peoples, that you should be mine (Leviticus 20:26).
In Leviticus 11, the Israelites were commanded not to eat swarming things. The idea of holiness is then equated with staying clean. Don't defile yourself. Don't make your hands dirty. Pontius Pilate washed his hands in front of the people. He handed Jesus over to them to be crucified. Could his conscience be clean? Well then, pay a hit man to kill someone you hate. Your hands are clean. But will your conscience? Obviously, something more needs be done.
In Leviticus 19, Moses was delivering the 10 commandments to the people of Israel. Now, the Israelites shall be holy when they keep the commandments of God. This is a step forward. More positive actions are included. Don't reap the field to its border or strip the vineyard bare. Leave the gleanings, the fallen grapes for the poor and the sojourners. The wage of the workers shall not remain with you till morning. Don't put a stumbling block before the blind. Don't hate your brother in your heart. Reason with your neighbour. Love your neighbour as yourself (Leviticus 19:18). The underprivileged are taken care of. In doing so, the Israelites shall be holy.
Leviticus 20 highlights another meaning of holiness. It is the separation from the rest of the world. People and things become holy when they are separated from the mundane and are dedicated exclusively to God. The Blessed Virgin Mary, for one, is holy. Her whole life was dedicated to God. Her womb was dedicated to God as the vessel to bear the Son of God. Her breasts exclusively fed baby Jesus (Luke 11:27). Jesus also calls her blessed because she hears the word of God and keeps it (Luke 11:28). The saints are holy men and women because they dedicated their life to God in different ways, in varying degrees. We Christians are called to be saints, to lead a life dedicated exclusively to God (Romans 1:7; 1 Corinthians 1:2). I think it is this concept of holiness which Peter refers to.
As obedient children, do not be conformed to the passions of your former ignorance,
but as he who called you is holy, be holy yourselves in all your conduct (1 Peter 1:14-15)

My Advocate, we lead a worldly life. Yet, we are called to separate ourselves from this world and dedicate ourselves to God. Make us Your holy Temple. Dwell in us so that we may pray with You in one accord. Our Lady, you are the purest and holiest of us all. Pray for your children that we may resemble your first born, our Lord, more closely. Amen.