yo vai mamātibharam āsura-vaṁśa-rājñām akṣauhiṇī-śatam apānudad ātmatantraḥ tvāṁ duḥstham ūnapadam ātmani pauruṣeṇa sampādayan yaduṣu ramyam abibhrad aṅgam
Synonyms
yaḥ—He who; vai—certainly; mama—mine; atibharam—too much burdensome; āsura-vaṁśa—belonging to the unbeliever class; rājñām—of the kings; akṣauhiṇī—One division of military phalanx consisting of*; śatam—such hundreds of divisions; apānudat—extirpated Atamatantrah—self sufficient; ātma-tantraḥ—unto you; tvām—put into difficulty; duḥstham—devoid of standing stength; ūnapadam—internal; ātmani—by dint of energy; pauruṣeṇa—for executing; sampādayan—in the Yadu dynasty; yaduṣu—transcendentally beautiful; ramyam—accepted Angam—body.
Translation
Oh the personality of religiousity, I was too much overburdened by the undue military phalanx of Akshouhini divisions by the kings of unbeliever class and I was relieved by the Grace of the Personality of Godhead. Similarly you were in distressed condition lessened by your standing strength and as such he also incarnated to get you relieved from such condition by His internal energy appearing in the family of the Yadus.
Purport
The Asura—class of men on the surface of the world want to enjoy life of sense gratifcation even at the cost of other's happiness. Inorder to fulfil this ambition of life the Asuras, specially the kings or the state executive heads, belonging to the unbeliever class of men, try to equip themselves with all kinds of deadly weapons preparing to bring about a war in the peaceful society. They have no other ambition than personal aggrandisemnt and as such the mother earth feels overburdened by such undue increase of military strength. By increase of such Asurik population the principles of religiosity becomes hamperred and the total result is that all the people of the world become unhappy, specially the devotee or Deva class of men feel too much for this anomalies of the Asurik civilization of self aggrandisement.
In such situation only the Personality of Godhead incarnates just to vanquish the unwanted Asuras and to re-establish the ture principles of religiosities. The misssion of the Lord Sri Krishna was this and He fulfilled it.