boasting: the act of saying out loud what you are proud of and counting on, whether that is yourself or God
This word names boasting as an activity: talking up whatever you are proud of and relying on. It is the noun that goes with the ordinary verb for boasting (καυχάομαι), and apart from one sharp line in James it belongs entirely to Paul.
Some of its uses are the boasting the New Testament shuts down. Paul asks what has become of boasting once God accepts people through faith, and answers that it has been shut out; James says every boast of that kind is evil. Other uses are boasting the New Testament is glad to own: Paul has a boast in Christ, and the boast he makes about his own conduct rests on God's kindness rather than on human cleverness. Same word, opposite verdicts, and the whole difference lies in what the boasting points to.
Its most distinctive use is Paul's proud pleasure in the churches he founded. He had boasted about the Corinthians to Titus and was relieved when they proved him right; he tells them their generosity will be the public proof of that boast; he calls the Thessalonians the crown he will boast in when Christ appears. Late in his second Corinthian letter the boasting turns back on himself, and he knows exactly how it sounds: he refuses to drop it, and calls it foolish talk in the same breath.
The word can also slide from the act of boasting to the thing being boasted about, so that a congregation or a clear conscience gets called someone's boast. Strictly that is the work of its close relative (καύχημα), but Paul moves back and forth between the two nouns inside a single argument, so the line between them is not one to lean on.