A somewhat literary or formal word for a feeling of great joy or triumph, often used in the phrase 快哉を叫ぶ (to shout with joy). Not common in casual speech.
He shouted with joy when he heard the news of his success.
From Chinese 快哉 (kuàizāi), literally 'joyful indeed'. The character 哉 is a classical exclamatory particle, giving the word a literary and somewhat archaic flavor.