Multinational corporations often conduct business in many countries (including their own home country) through operating subsidiaries established for particular countries. As long as all legal formalities are strictly observed (to preclude piercing the corporate veil), this will limit the parent's exposure to a local legal system (liability, tax, etc.), since from a domestic perspective, the parent is merely a majority shareholder of a local corporation's stock.
In the U.S. banking industry, the term refers to a subsidiary of a bank through which the bank chooses to indirectly conduct some part of its banking business (or related businesses like insurance). To prevent banks from concealing their true structure or strength from regulators, they are required to give public notice of certain transactions with certain operating subsidiaries.
In the U.S. railroad industry, the term refers to a company that is a subsidiary but operates with its own identity and rolling stock. In contrast, a non-operating subsidiary would exist on paper only, but for operating purposes would use the identity and rolling stock of the parent company.