sva-amśa - of personal expansions; vibhinna-amśa - of separated expansions; rūpe - in the forms; hañā - becoming; vistāra - expanded; ananta - unlimited; vaikuṇṭha - in the spiritual planets known as Vaikuṇṭhas; brahmāṇḍe - in the material universes; karena vihāra - performs His pastimes.

“Kṛṣṇa expands Himself in many forms. Some of them are personal expansions, and some are separate expansions. Thus He performs pastimes in both the spiritual and the material worlds. The spiritual worlds are the Vaikuṇṭha planets, and the material universes are the brahmāṇḍas, gigantic globes governed by Lord Brahmā.