Veda means the Vedic literatures. Veda, real literal meaning is, veda means knowledge. Vetti veda vido jñāne. There is a Sanskrit root, vid-dhātu. From that vid-dhātu, veda. Veda means knowledge. And purāṇa, purāṇa means supplementary; Vedic instruction described in story form. That is called purāṇa, story. This Bhāgavata is also one of the Mahā-purāṇa. Mahā-purāṇa means the science of Kṛṣṇa is described in story form. This is called purāṇa. People better understands in stories, in history.
So Lord Caitanya says: "Because people in general, by the influence of the illusory energy, they have forgotten their eternal relationship with the Supreme Lord, therefore the Lord Himself, as Kṛṣṇa-dvaipāyana Vyāsa . . ." Kṛṣṇa-dvaipāyana Vyāsa is considered to be a powerful incarnation of Kṛṣṇa. Unless he was a, he was an incarnation, it was not possible to write so many books. There are eighteen Purāṇas and four Vedas and 108 Upaniṣads, and Vedānta, then Mahābhārata, then Śrīmad-Bhāgavatam. Each of them contains thousands and thousands and millions of verses. So we cannot imagine that a man can write in that way. You see?
So Veda-vyāsa is considered to be incarnation of Kṛṣṇa, and he was very powerful in writing.