G-d makes us holy when we fulfill His Mitzvot — commandments.
Mitzvah means commandment, but it is also related to the word “tzavso — bonding.” By performing a physical Mitzvah in this physical world, we bond with G-d, drawing His holiness to us.
Chassidus teaches that the highest comes into the lowest. The Medrash tells us that G-d desired a dwelling place down below, in our world. Our souls were sent down into physical bodies, in order to learn Torah and do Mitzvot. By doing so, we bring G-d’s holiness into ourselves, and into the world around us.
We thus hasten the final Redemption with Moshiach, when G-dliness will shine everywhere, and this world becomes His dwelling place.