• vaṁśaḥ — the dynasty
  Lineage. Gauḍīya note: the Yadu-vaṁśa is special because Kṛṣṇa took birth in it; SB 1.3.28 (kṛṣṇas tu bhagavān svayam) is implicit context. Where Bhagavān walks, the family-line becomes śāstra-listed.
• yadoḥ — of King Yadu
  Yadu was the son of Yayāti and the patriarch of this lineage (cursed by his father to never inherit the throne but blessed in a deeper way — Bhagavān eventually appeared in his line). Bhāgavata grace: the curse becomes the kṣetra for Kṛṣṇa's appearance.
• parirakṣitaḥ — protected on all sides
  Pari- prefix — protected entirely, in every direction. Kṛṣṇa's rakṣaṇa is never partial. Gītā 9.22 (yoga-kṣemaṁ vahāmy aham) is the same teaching: Bhagavān carries both the getting and the keeping of His devotees' welfare.
• mahatvam — power
  Greatness, glory. Gauḍīya caution: when applied to a Vaiṣṇava-lineage, mahatva is read as Bhagavān's own greatness manifesting through them, not as their independent aiśvarya.

The Yadu dynasty under Kṛṣṇa's full protection is named famous-by-protection — parirakṣitaḥ. This is bhakti's ordinary fruit at the social register: a house Kṛṣṇa shelters becomes a house of fame and dharma. The same protection that held Govardhana over the gopas now holds the whole vaṁśa.