International law refers to the system of implicit and explicit agreements made outside a nation. For example the United States often makes agreements with other countries. Companies and the government need an international lawyer to make these agreements. The international lawyer reviews the agreements being made. They may even make suggestions of how to make it better. The international lawyer you find may deal in public, private, or supranational international law.
Typically an international lawyer is going to be industry specific. It could be important for a business to have more than one international lawyer on the payroll to ensure the laws are being followed. Traditionally there are two branches called jus gentium the law of nations, and then jus inter gentes or agreements among nations.