What is the principle of the rule on a contract where a party is bound by their own word?

Genesis of the rule may be read in Lord Denning M.R.'s The Discipline of Law (1979), where, at pp. 208-9, and quoting from his own remarks in Combe v. Combe, [1951] 2 K.B. 215 at p. 220, that recently retired and very learned jurist said: The principle, as I understand it, is that, where one party has, by his words or conduct, made to the other a promise or assurance which was intended to affect the legal relations between them and to be acted on accordingly, then, once the other party has taken him at his word and acted on it, the one who gave the promise or assurance cannot afterwards be allowed to revert to the previous legal relations as if no such promise or assurance had been made by him, but he must accept their legal relations subject to the qualification which he himself has so introduced, even though it is not supported in point of law by any consideration but only by his word. Seeing that the principle never stands alone as giving a cause of action in itself, it can never do away with the necessity of consideration when that is an essential part of the cause of action. The doctrine of consideration is too firmly fixed to be overthrown by a side-wind. Its ill-effects have been largely mitigated of late, but it still remains a cardinal necessity of the formation of a contract, though not of its modification or discharge."