Bhagavān Kṛṣṇa continues the yajña-cycle. In the previous shloka, he showed the chain: beings depend on food, food comes from rain, rain comes from yajña, and yajña comes from karma. Now he explains where this karma-yoga way of life is known from.

Karma brahmodbhavam means karma is born from brahma, and here brahma means the Veda. The harmonious life of karma-yoga — a life of sacrifice, sharing, dānam, yajña, and responsibility — is taught by the Veda. Human beings may not discover this complete dhārmic order merely through personal preference or changing social theories. The Veda reveals how to live in harmony with the whole.

Then Bhagavān says brahmākṣarasamudbhavam — the Veda itself is born from akṣaram, the Imperishable Bhagavān. This is important because the Veda is not treated as a human invention. Human intellect has limits. Human ideas change from time to time. But the Vedic teaching has the authority of Bhagavān’s vision of creation. The creator alone fully knows how creation is to be handled.

Therefore, Bhagavān says tasmāt sarvagataṁ brahma — therefore the Veda is all-pervading. In a Vedic society, Vedic teaching enters every part of life: eating, study, family, work, dānam, rituals, hospitality, ecology, duties, values, and spiritual pursuit. It is not confined to a temple or a book.

Finally, nityaṁ yajñe pratiṣṭhitam means the Veda is always established in yajña. Wherever there is genuine sacrifice, sharing, offering, service, and dānam, there the Vedic teaching is alive. If the Veda is only recited but not lived through yajña, its spirit is missed. If a person lives a life of contribution and offering, that person is participating in the Vedic vision.

So the teaching of 3.15 is: karma-yoga is not a personal opinion, social fashion, or optional moral preference. It is the Vedic way of maintaining harmony, and the Veda itself comes from Bhagavān. Therefore a life of yajña is sacred, authoritative, and necessary.