Minority interest refers to the  amount of interest of subsidiaries that belongs to shareholders other than the parent company.

A subsidiary is a company that is owned / or controlled by the holding company. Suppose Roma as a business entity owns 100% of shares of Italiano. Here Roma is the holding company and Italiano is the subsidiary company. In this case the holding company has complete right over the profits as well as assets of Italiano. Suppose Roma holds 75% of shares of Italiano whereas 25% of the shares are held by the previous owners. While Roma is still the holding company and Italiano the subsidiary, Roma is now  entitled to only 75% of the profits and assets of Italiano whereas the rest accrues to the other shareholders. 25% of the value of the company is shown in the balance sheet of Roma as minority interest under liabilities.