oath: a solemn sworn word that binds the speaker, calling on God as guarantor
An oath is a binding word. When someone swears one, they call on God to hold them to what they say, so that their promise can no longer be taken back. Ancient readers even heard in the word the idea of a fence or a restraint: an oath hems the speaker in. Built into it is a hidden threat against the speaker's own self, since to swear falsely is to invite God's punishment on your own head.
The New Testament pulls this one word in two directions depending on who is speaking. When people swear, it tends to go wrong. Herod is trapped by the oaths he blurted out at a party and has John the Baptist killed rather than lose face. Peter swears he never knew Jesus, and the sworn word is the one that proves false. Because of this, Jesus tells his followers to stop swearing altogether and simply let their yes mean yes, and James repeats the command almost word for word. The point is not that promises are bad, but that a community whose plain word is fully trustworthy has no need to prop it up with oaths.
When God is the one who swears, the very same word becomes the ground of hope. God cannot appeal to anyone greater, so he swears by himself, and the letter to the Hebrews makes this the anchor of Christian confidence: God has bound his own promise beyond any possibility of change. The oath God swore to Abraham and to David runs through the songs and sermons of the early church as the reason his rescue cannot fail.
Several close relatives sit nearby. The plain verb for the act of swearing is ὄμνυμι, and Hebrews uses a separate, weightier word for the solemn ceremony of oath-taking, ὁρκωμοσία. Behind the Greek stand two Hebrew words this one absorbs: שׁבועה, a sworn promise, and אלה, an oath that carries a curse.