kṛṣṇa-avatāre - in the incarnation of Lord Kṛṣṇa; jyeṣṭha hailā - He became the elder brother; sevāra kāraṇa - for the purpose of service; kṛṣṇake - to Kṛṣṇa; karāila - made; nānā - various; sukha - happinesses; āsvādana - tasting.

When Lord Kṛṣṇa appeared, He [Balarāma] became His elder brother to serve Him to His heart’s content and make Him enjoy all sorts of happiness.