Bhashya
स तस्मिन्नेव शरीरे गतमनः सन्किमकरोदिति, उच्यते— सोऽकामयत ।कथम् ? मेध्यं मेधार्हं यज्ञियं मे मम इदं शरीरम् स्यात् ; किंच आत्मन्वी आत्मवांश्च अनेन शरीरेण शरीरवान् स्यामिति— प्रविवेश ।यस्मात् तच्छरीरं तद्वियोगाद्रतयशोवीर्यं सत् अश्वत् अश्वयत्, ततः तस्मात् अश्वः समभवत् ; ततोऽश्वनामा प्रजापतिरेव साक्षादिति स्तूयते ; यस्माच्च पुनस्तत्प्रवेशात् गतयशोवीर्यत्वाद्मेध्यं सत् मेध्यमभूत्, तदेव तस्मादेव अश्वमेधस्य अश्वमेधनाम्नः क्रतोः अश्वमेधत्वम् अश्वमेधनामलाभः ; क्रियाकारकफलात्मको हि क्रतुः ; स च प्रजापतिरेवेति स्तूयते ।
In plain words
He entered that very body, his mind fully absorbed, and asked: What is to be done? He desired: May this body of mine become pure and fit for sacrifice, and may I be fully embodied within it. With this thought, he entered. Because that body lacked glory and vitality in his absence and cried out, the horse was born from it; and thus it is directly glorified as Prajāpati, bearing the name of the horse. And because that very body, upon his entry, regained its sacred fitness, that ritual acquired its name and nature as the great horse-sacrifice—for every sacrifice consists of action, means, and fruit, and that sacrifice is indeed none other than Prajāpati.
Close to the Sanskrit
He residing in that very body having entered with mind, what did he do, is said: He desired. How? May this body of mine be fit for sacrifice, worthy of oblation, sacrificial, and may I, endowed with self and possessing a self, be embodied with this body, thus—he entered. Because that body, being stripped of glory and vigor through separation from him, lamented, therefore from that the horse came into being; thence he is praised directly as Prajāpati named horse; and because that very thing, through that entry, having lost its glory and vigor, became fit for sacrifice, therefore alone the horse-sacrifice's being an horse-sacrifice and the attainment of the name horse-sacrifice belong to that sacrifice of the nature of action, instrument, and fruit; and that is praised as Prajāpati indeed.