move out
To leave your home and take your things to live elsewhere.
To move out means to pack up your belongings and leave the place where you've been living. When someone moves out of an apartment or house, they take their furniture, clothes, and possessions with them because they're going to live somewhere else.
College students move out of their dorm rooms at the end of the school year. When children grow up and become adults, they eventually move out of their parents' house to live on their own. A family might move out of their old house after they've bought a new one in a different neighborhood.
Moving out usually involves packing everything, cleaning the place, returning keys, and making sure you haven't left anything behind. It's different from simply leaving for a trip or visiting someone: when you move out, you're changing where you actually live. The opposite is moving in, which is when you arrive at a new place with your belongings and start living there.