In plain words
Among horses know Me as Ucchaihshravas, born of nectar; among lordly elephants I am Airavata; among human beings I am the king.
Word for word
Uccaiḥśravas among horses know Me [to be], born of [the churning for] amṛta; Airāvata among lordly elephants; and among men, the ruler of men.
The commentators
Bhagavadgītābhāṣyam· bhāṣya
उच्चैःश्रवसम् अश्वानां उच्चैःश्रवाः नाम अश्वराजः तं मां विद्धि विजानीहि अमृतोद्भवम् अमृतनिमित्तमथनोद्भवम् । ऐरावतम् इरावत्याः अपत्यं गजेन्द्राणां हस्तीश्वराणाम् , तम् ‘मां विद्धि’ इति अनुवर्तते । नराणां च मनुष्याणां नराधिपं राजानं मां विद्धि जानीहि ॥ २७ ॥
In plain words
Uccaiḥśravas: among horses, the horse called Uccaiḥśravas, king of them all — know that one as Me. And amṛtodbhava means born of the churning that was undertaken to win the nectar. Airāvata: the child of Irāvatī. Among the great elephants, the lords of elephants, he is the one — and here 'know as Me' still applies. And among men, among human beings, know Me as narādhipa, the king.
Close to the Sanskrit
Uccaiḥśravasam — of horses, the horse-king named Uccaiḥśravas; him know as Me, understand; amṛtodbhavam — arisen from the churning undertaken for the sake of the nectar. Airāvatam — the offspring of Irāvatī; of lordly elephants, of the masters of elephants — of him, 'know as Me' carries over. And of men, that is, of human beings, know Me, understand Me, as narādhipa, the king.