A treaty is a formal written agreement between two or more sovereigns or nations. It is essentially a contract between countries or heads of states. The Vienna Convention on the Law of Treaties (VCLT), which prescribes the procedures for how to apply and interpret treaties, defines treaties as "an international agreement concluded between States in written form and governed by international law." (While the United States is not a party to the VCLT, it has taken the position that the VCLT codifies rules of customary law regarding the operation and interpretation of treaties.)
Treaties come in two forms: bilateral and multilateral.
Bilaterial treaties are treaties between only two nations. The extradition treaty between France and the United States (TIAS 02-201) is an example of a bilateral treaty. It only applies to France and the U.S.
Multilateral treaties are treaties among more than three or more nations. The treaty regarding polar bear conservation among the U.S., Canada, Denmark, Norway, and Russia (27 UST 3918) is an example of a multilateral treaty. It applies to all five of the above nations.
Ratification of treaties require both signature AND consent to be bound. The signature testifies that the signed convention is a genuine and authentic document agreed to by the negotiating parties. Consent to be bound is shown when a signed instrument expressing consent is submitted.
The three typical means of expressing consent to be bound are ratification, access, and acceptance/approval.
Entry into force: Even after ratification, the convention doesn't become legally binding on the state. A multilateral treaty will usually outline the conditions required for the treaty to come into force in one of the articles of the treaty.
States do not always agree to all the terms of a treaty, and express that in one of several ways.
Reservations: State wants to sign the treaty, but disagrees on one or more terms of the treaty.
Declarations/understandings: State wants to make clear its interpretation of specific terms of a treaty that it considers vague or ambiguous.
Exclusions/exceptions: State wants to exclude application of the treaty to a particular geographical sub-unit of the state.