A promisor is a party who makes a promise. The opposite of course the promise (the party to whom a promise is made).
The use of promisor and promisee are used extensively in the area of contract law. The or and ee construction makes it easier for lawyers and judges to concentrate on the abstract formulation of the law while incorporating the bare facts needed to access how the law should be applied. In other words, the names of the parties involved in a contract dispute are not important. What is important is what action they take within the facts to be analyzed under the law. Adding additional facts to the analysis may only confuse the basic application of the law.
Of course, the use of the construction can also be used simply to explain the law or a particular aspect of the law an example of such being a description of consideration in contract: “The doctrine of consideration provides that a promise will bind the promisor only if it is given as the price for another’s promise or as the price for an action which involves a detriment to the promisee.”