What is the correct term for an agreement that ends the obligation of both parties in a contract?

The correct term for an agreement that ends the obligation of both parties in a contract is "Rescission." Rescission is a legal remedy that allows for the cancellation of a contract, thus relieving both parties of their obligations under that contract. This often occurs when both parties mutually agree to void the contract or when the contract is deemed voidable due to issues such as misrepresentation or coercion.

Understanding this concept is crucial because it helps clarify situations where an existing agreement can be nullified, and both parties can go back to their previous positions, as if the contract had never been made. The other terms presented in the question have different meanings: termination refers to ending a contract but may not necessarily release both parties from obligations entirely, modification involves changing the terms of the contract rather than cancelling it, and severance pertains to removing a part of a contract while keeping the rest intact. Therefore, "Rescission" accurately reflects the agreement that fully concludes the contract and its obligations.