An agreement is an informal term for a de facto contract, which is generally a promise in exchange for something. Laws require certain agreements to be in writing in order to be enforceable. A legally enforceable agreement is known as a contract. An agreement means mutual consent.
An agreement can have a meaning that is more broad than contract. For example, an agreement can be a gift, or any promise without obtaining something in return.
Another example is an agreement in an argument, which implies no contract. For example, two people might agree that George Bush is a good president.