Negatively, conceitedly praising oneself. Positively, trusting and exulting in who God is, and what he has done.
Boasting condemned
See also
Boasting exposed as folly
Salvation by faith means no-one can boast about human merit
Examples of foolish boasting
Nebuchadnezzar
Simon the sorcerer
the antichrist
Legitimate boasting
Boasting in God
Boasting in the results of ministry
Boasting in the conduct of ministry