International Law, according to the Restatement of the Law (Third), the Foreign Relations of the United States, "consists of rules and principles of general application dealing with the conduct of states and of international organizations and with their relations inter se, as well as with some of their relations with persons, whether natural or juridical."
More basically, international law refers to the law governing interactions between nations. There are two types of international law: public and private.
Public International law focuses on relationships between nations and citizens of different nations as governed by various inter-governmental organizations, such as the United Nations and NATO, and other sources of law such as treaties and custom. For example, a dispute over a waterway between two nations would be governed by Public International law.
Private International law is synonymous with the concept of "conflict of laws"; that is, it refers to legal disputes, typically involving private citizens, in which jurisdictional issues are the primary area of inquiry. For example, a contract dispute between citizens of two different countries would likely be governed by Private International law.
Text from UCLA's (Hugh & Hazel Darling Law Library, UCLA Law School) Researching Public International Law page.
What are the sources of international law? The following statements give some guidance. For more on the sources of international law see any introduction to international law.
The Classic List: Statute of International Court of Justice, Article 38, § 1
International conventions [i.e., treaties and agreements].
International custom, as evidence of a general practice accepted as law.
The general principles of law recognized by civilized nations.
Judicial decisions and the teachings of the most highly qualified publicists of the various nations, as subsidiary means for the determination of rules of law.
Restatement of the Law, the Foreign Relations Law of the United States, § 102
Customary law, which "results from a general and consistent practice of states followed by them from a sense of legal obligation.'
General principles common to the major legal systems.