umm sorry to cerrect here, ima real stickler for details,as sanskrit is very precise, but it literally means:

om--O my Lord; namah--my respectful obeisances unto You; bhagavate--unto the Personality of Godhead; vasudevaya--unto Lord Krsna, the son of Vasudeva.

TRANSLATION

O my Lord, the all-pervading Personality of Godhead, I offer my respectful obeisances unto You.

hope that helps.

Intoning universal peace in the name of the godhead Vasu unto he who would manifest it.

For an elaboration of the verse please see Srila Vyasadeva's, KrishnaDvaipanaya Vyasa's great ancient work the Bhagavata Purana, Srimad Bhagavatam.

It is invocated and elaborated nicely in the first verse.

srimadbhagavatam.com/1/1/1/en
Śrīmad Bhāgavatam 1.1.1

oḿ namo bhagavate vāsudevāya

janmādy asya yato 'nvayād itarataś cārtheṣv abhijñaḥ svarāṭ

tene brahma hṛdā ya ādi-kavaye muhyanti yat sūrayaḥ

tejo-vāri-mṛdāḿ yathā vinimayo yatra tri-sargo 'mṛṣā

dhāmnā svena sadā nirasta-kuhakaḿ satyaḿ paraḿ dhīmahi

SYNONYMS

om — O my Lord; namaḥ — offering my obeisances; bhagavate — unto the Personality of Godhead; vāsudevāya — unto Vāsudeva (the son of Vasudeva), or Lord Śrī Kṛṣṇa, the primeval Lord; janma-ādi — creation, sustenance and destruction; asya — of the manifested universes; yataḥ — from whom; anvayāt — directly; itarataḥ — indirectly; ca — and; artheṣu — purposes; abhijñaḥ — fully cognizant; sva-rāṭ — fully independent; tene — imparted; brahma — the Vedic knowledge; hṛdā — consciousness of the heart; yaḥ — one who; ādi-kavaye — unto the original created being; muhyanti — are illusioned; yat — about whom; sūrayaḥ — great sages and demigods; tejaḥ — fire; vāri — water; mṛdām — earth; yathā — as much as; vinimayaḥ — action and reaction; yatra — whereupon; tri-sargaḥ — three modes of creation, creative faculties; amṛṣā — almost factual; dhāmnā — along with all transcendental paraphernalia; svena — self-sufficiently; sadā — always; nirasta — negation by absence; kuhakam — illusion; satyam — truth; param — absolute; dhīmahi — I do meditate upon.

TRANSLATION

O my Lord, Śrī Kṛṣṇa, son of Vasudeva, O all-pervading Personality of Godhead, I offer my respectful obeisances unto You. I meditate upon Lord Śrī Kṛṣṇa because He is the Absolute Truth and the primeval cause of all causes of the creation, sustenance and destruction of the manifested universes. He is directly and indirectly conscious of all manifestations, and He is independent because there is no other cause beyond Him. It is He only who first imparted the Vedic knowledge unto the heart of Brahmājī, the original living being. By Him even the great sages and demigods are placed into illusion, as one is bewildered by the illusory representations of water seen in fire, or land seen on water. Only because of Him do the material universes, temporarily manifested by the reactions of the three modes of nature, appear factual, although they are unreal. I therefore meditate upon Him, Lord Śrī Kṛṣṇa, who is eternally existent in the transcendental abode, which is forever free from the illusory representations of the material world. I meditate upon Him, for He is the Absolute Truth.


In the link there is an elaborate purport.