If you are simply asking what makes a contract valid under our existing legal system, the answer is “consideration.” A unilaterial promise to do something is not binding. However, if A promises to do X, and, in exchange, B promises to do Y, then there is “consideration.” This is often referred to as “quid pro quo,” and it is essentially a way of saying that each party must agree to both give and get something as part of the transaction.
It is important to realize that “consideration” is not limited to exchanges of property (as someone suggested in this thread). One person may give property (e.g., money, a dog, a loaf of bread), and the other may give a service (e.g., mow the lawn, wash the windows, do the other party’s taxes). Moreover, even if one party agrees to forego something to which it would otherwise be entitled, that would be enough. For example, if person A has the right to sue person B over some matter, the two parties may enter into a settlement contract whereby person A agrees to forego his right to sue B, and, in exchange, person B agrees to pay some money or take some action, etc. That would be enough for “consideration” to be present.
Again, if one person promises to do something but the the recipient of the promised benefit does not promise to give anything in return (or promise to give up something to which that person is otherwise entitled), then there is no consideration, and the promise is not a contract (and is therefore not binding).