When something is described as multinational, it involves more than two countries. A multinational corporation buys and sells in several countries, and it may also have offices in these countries.
A multinational conflict is a war that involves the governments of three or more countries. Multinational peacekeepers might be from an organization like the United Nations (which could also be described as a multinational organization), working in many countries toward a peaceful agreement between them. The adjective multinational uses the prefix multi-, or "many," adding it to national, from the Latin nationem, "birth, kind, or tribe."