Question: "What does the Bible say about holiness? What does it mean to be holy?"
Answer: In 1 Peter 1:13-16, Peter writes to believers, "Therefore, prepare your minds for action, keep sober in spirit, fix your hope completely on the grace to be brought to you at the revelation of Jesus Christ. As obedient children, do not be conformed to the former lusts which were yours in your ignorance, but like the Holy One who called you, be holy yourselves also in all your behavior; because it is written, 'You shall be holy, for I am holy.'" Peter is quoting from Leviticus 11:44 and Leviticus 19:2.
First, let's look at God's holiness. What does it mean that God is holy? Passages like 1 Samuel 2:2 and Isaiah 6:3 are just two of many examples of passages about God's holiness. Another way to say it is absolute perfection. God is unlike any other (see Hosea 11:9), and His holiness is the essence of that "otherness." His very being is completely absent of even a trace of sin (James 1:13; Hebrews 6:18). He is high above any other, and no one can compare to Him (Psalm 40:5). God's holiness pervades His entire being and shapes all His attributes. His love is a holy love, His mercy is holy mercy, and even His anger and wrath are holy anger and holy wrath. These concepts are difficult for humans to grasp, just as God is difficult for us to understand in His entirety.
Next, what does it mean for us to be holy? When God told Israel to be holy in Leviticus 11 and 19, He was instructing them to be distinct from the other nations by giving them specific regulations to govern their lives. Israel is God's chosen nation and God has set them apart from all other people groups. They are His special people, and consequently they were given standards that God wanted them to live by so the world would know they belonged to Him. When Peter repeats the Lord's words in 1 Peter 1:16, he is talking specifically to believers. As believers, we need to be "set apart" from the world unto the Lord. We need to be living by God's standards, not the world's. God isn't calling us to be perfect, but to be distinct from the world. First Peter 2:9 describes believers as "a holy nation." It is a fact! We are separated from the world; we need to live out that reality in our day-to-day lives, which Peter tells us how to do in 1 Peter 1:13-16.
Finally, how can we become holy? Holiness only results from a right relationship with God by believing in Jesus Christ as Savior (accepting His gift of eternal life). If we have not placed our faith in God's Son alone to save us from our sins, then our pursuit of holiness is in vain. So, we must first make sure we are born-again believers (see John 3). If we truly are believers, then we recognize that our position in Christ automatically sets us apart from the world (1 Peter 2:9). After all, we have a relationship with the living God! Then we must daily live a set-apart life, not trying to "blend in" with the world, but instead living according to God's Word as we study the Bible and grow in it.