A parent company is a company that has controlling influence in one or more companies. These companies are called subsidiaries.
Another name for a parent company is a holding company.
In order for a company to be considered a parent company, they must own over 50 percent of the shares in the subsidiary. Another way is if the company has controlling influence through an agreement with the other owners of the subsidiary.
Many parent companies will often only function to own shares in other companies, and then it is called a holding company. A parent company can also operate its own business independently or together with its subsidiaries. This is entirely up to the company itself. A holding company will usually have the intention of only owning shares in the subsidiaries.