The Vienna Convention on the Law of Treaties (.pdf) defines a treaty as "an international agreement concluded between States in written form and governed by international law, whether embodied in a single instrument or in two or more related instruments and whatever its particular designation."
Treaties can be referred to by a number of different names: international conventions, international agreements, covenants, final acts, charters, memorandums of understandings (MOUs), protocols, pacts, accords, and constitutions for international organizations. Usually, these different names have no legal significance in international law.
Treaties may be bilateral (two parties) or multilateral (between several parties) and a treaty is usually only binding on the parties to the agreement. An agreement "enters into force" when the terms for entry into force as specified in the agreement are met. Bilateral treaties usually enter into force when both parties agree to be bound as of a certain date.
For definitions of key terms, see the U.N. Treaty Reference Guide.
In the United States, the term "treaty" is used specifically to refer to the small number of international agreements that require the advice and consent of the Senate before entering into force. In contrast, "executive agreements" do not require Senate consent. Both types of agreements are binding under international law. For more information on the distinction between the two, consult this helpful guide from the Georgetown Law Library.