If you're triumphant, you're proud of a huge success, like your triumphant victory at your ping-pong tournament.
Winning an honor or a competition means that you're triumphant. The joy you feel about your win is described as triumphant. You might flash a triumphant smile at the audience during the curtain call after your excellent performance in the school play. Triumphant comes from the Latin word triumphus, which means triumph, but also describes a procession for a victorious general or admiral.