Private equity is an alternative asset class with investors that raise money from institutional investors and then use that capital to purchase equity in companies with the hope of selling the equity or the whole company at a profit years later. (Carta)
Privately owned companies are owned by private citizens, generally families or individuals. Often the owners of the company are the founders or family of the founders. It means that the company is not bought and sold on any stock exchange; allowing the company to operate in the long-term interest of the company and it's employees and consumers rather than driving never ending growth to pay back investors (stockholders).