• pradyumnaḥ — Pradyumna
  Pra + √dyut — 'shining forth.' Kṛṣṇa's first son, an expansion of Vāsudeva according to the Pāñcarātra catur-vyūha (Vāsudeva, Saṅkarṣaṇa, Pradyumna, Aniruddha). When Pradyumna fights, an aṁśa of Bhagavān fights.
• bhagavān — the Lord
  Applied here to Pradyumna. The Bhāgavatam reserves bhagavān for full Godhood, but extends it to Pradyumna because of his catur-vyūha status. Important Gauḍīya note: Bhagavān-hood is shareable through expansion, never through merging.
• mā bhaiṣṭa — do not fear
  Imperative + negative particle. The signature reassurance in Bhāgavata-rakṣaṇa moments — Kṛṣṇa says it to Yaśodā (10.7), to the gopas at Govardhana (10.25). In a Vraja-rasa key, mā bhaiṣṭa is Bhagavān's first kindness.
• ratha-ārūḍhaḥ — mounted on His chariot
  Contiguous join (ratha + ārūḍhaḥ). Echoes Arjuna ratha-sthaḥ in Gītā 1. In Kaṭha Upaniṣad 1.3.3 the body is the chariot and ātmā the rider; here Pradyumna takes ratha as the warrior, but Gauḍīyas read every Bhāgavata chariot through that Upaniṣadic frame.
• mahā-yaśāḥ — whose glory is immense
  Contiguous join (mahā + yaśāḥ). Yaśas — fame that survives the fame-holder. Pradyumna's yaśas is not earned by today's deed; the verse calls him mahā-yaśas as a stable epithet — fame already established by his Śambara-killing past.

Like the eldest son who steps to the door when his Father is occupied within, Pradyumna mounts His chariot and tells the citizens 'do not fear' — the same mā bhaiṣṭa that Kṛṣṇa breathes everywhere, now spoken by His son for the first time on the battlefield of Dvārakā.