If the Torah commands us "You shall be holy, for I, Hashem your God, am holy," but God's holiness is infinite and absolute while ours is limited and human — what does it actually mean for us to imitate divine holiness, and how can we possibly bridge that unbridgeable gap?

This is an excellent question that goes to the heart of our purpose as Jews. When Hashem commands us "Kedoshim Tihyu Ki Kadosh Ani" - "You shall be holy for I am holy" - He is not telling us we can become holy like Him. That would be impossible. Hashem's holiness is infinite and absolute. We can never reach His level. The Midrash explains this clearly. When Hashem says "I am holy," He means exactly what Pharaoh meant when he told Yosef HaTzadik "I am Pharaoh" - meaning you will have authority, but only up to a point. My greatness is above your greatness. Similarly, Hashem is telling us: you can be holy, but up to a point. You can never be like Me. So what does it mean to be holy? It means to emulate Hashem's behavior and character traits - His middot. Just as He is compassionate, you be compassionate. Just as He is merciful, you be merciful. Just as He is generous, you be generous. Just as He is honest, you be honest. The Ramban teaches us that our attempt to acquire holiness is an obligation because that is the way we serve Him - by emulating Him. This is a mitzvah, not a suggestion. When you follow the Torah and do what is good and righteous, you sanctify His great name. You make yourself holy by learning Torah and doing the mitzvot. The first mitzvah in the Torah is to know Hashem, and you know Hashem by learning His ordinances. But there is something more specific here. Rashi explains that whenever the Torah mentions holiness, it always refers to the issues of morality - specifically how we conduct ourselves in matters of intimacy and modesty. The Ramban adds that holiness is not just about avoiding what is forbidden, but also knowing limits even in what is permitted. You should not be like a pig that eats anything kosher, or a rooster that mates just because your wife is next to you. Holiness means conducting yourself with restraint and sanctity even in permitted matters. This is the foundation. Holiness begins with how we express our sensuality, how we protect our eyes, our speech, our minds, what we admire and look up to. When you sanctify yourself in these areas, you are imitating Hashem's holiness on the level that is possible for human beings. The gap you mention is bridged through our actions, not through our essence. We cannot change our nature to become infinite like Hashem, but we can change our behavior to reflect His character. When a servant tries to emulate his master, he does not become the master - but he becomes a good servant by acting according to the master's preferences rather than his own. This is our path. Even trying to be holy is in itself an act of holiness. You do not need to reach the level of Moshe Rabbeinu. Hashem commanded us to at least aspire to be better. Everyone is on their own level, but everybody can reach somewhere better than where they are right now. Start where you are, work on perfecting your character traits, control your desires, and sanctify yourself step by step. That is how we bridge the gap - not by becoming God, but by becoming His holy servants.