Which of the following terms refers to an agreement between two parties that is legally binding?

The term that refers to an agreement between two parties that is legally binding is indeed a contract. A contract is a formal agreement that creates enforceable obligations on the part of the parties involved. It typically requires certain elements to be considered valid, such as mutual consent, consideration (something of value exchanged), and a lawful purpose.

In contrast, the other options represent differing levels of commitment or understanding but do not have the legal enforceability associated with a contract. An understanding implies a mutual recognition of a situation but lacks the formal requirements that would make it legally binding. A promise is a commitment to act or refrain from acting in a certain way but is also not necessarily enforceable in a legal sense without additional context. A commitment denotes a strong personal intention or pledge to do something but lacks the specific legal framework that characterizes a contract. Thus, the correct answer, contract, aligns with the definition of a legally binding agreement in legal terms.