to promise: to declare, with a commitment that binds the speaker, that one will give or do something
The word means to promise: to state, in a way that binds the one speaking, that a thing will be given or done. In the New Testament the striking pattern is who does the promising. Again and again the subject is God, who promised land to Abraham, eternal life before the ages began, a crown of life, and a kingdom to those who love him. Because the one promising is God, the word carries a weight of certainty that an everyday promise lacks.
The same verb also covers ordinary human promises. Those who paid Judas promised him money, and false teachers promise their followers a freedom they cannot deliver. The verb itself means the same thing in every case; what changes is who is speaking and whether the promise can be kept.
The related noun (ἐπαγγελία) names the promise itself, and it became one of the central words of New Testament faith, gathering up everything God has pledged to his people.