Conflict of laws is an area of the law, the subject matter taught to law students, and which purport to set out, in a long list of rules, how to resolve private disputes which include an international or foreign element.
An excellent description is provided in the British law book Dicey and Morris on Conflict on Laws (London: Sweet & Maxwell, 2000):
"The branch of English law known as conflict of laws is that part which deals with cases having a foreign element. By a 'foreign element' is meant simply a contact with some system of law other than English law. Such a contact may exists, for example, because a contract was made or to be performed in a foreign country, or because a tort was committed there, or because property was situated there, or because the parties are not English."
With changes on points of detail, that description fits every jurisdiction.
International lawyers and jurists bicker over whether to refer to this branch of law as private international law or 'conflict of laws', both meaning the same thing. The former is far more self-explanatory, user-friendly and preferred by civil law jurisdictions; whereas the later has the blessing of both the British, and most of the American justice system.