The Vedas are the most ancient and most important of all Hindu sacred literature. There are four Vedas, although only three are mentioned in the Buddhist scriptures (M.II,133). They are the èg Veda, the Sāma Veda, the Yajur Veda, all composed between the 13th and 7th century BC, and the Atharva Veda, included into the sacred canon only several centuries after the Buddha.
The Vedas are believed by Hindus to be an eternal (sanātana) revelation (śruti) of divine origin (apauruṣeya). Those who deny the authority of the Vedas are said to be 'impure' (nāstaka). The Buddha said that nothing is eternal, he considered revelation to be an unreliable means of knowledge and he rejected the idea of a supreme god as unconvincing. He also cast serious doubts on the claim that the authors of the Vedas had divine knowledge. Once a brahman asked him what he thought of the belief that the authors of the Vedas had direct experience of the divine. The Buddha replied, 'What do you think about this? Is there one brahman who says, “I know. I see. This alone is true, all else is false?”
Did any of the teachers of the brahmans or even their teachers going back through seven generations ever say that?
Then what of ancient brahman sages who composed the Vedic hymns, who chanted, uttered and compiled them and which the brahmans of today still chant and recite, just repeating what has been repeated and chanting what has been chanted? Did they ever say “We know. We see. This alone is true, all else is false?”
No Gotama. They did not.
Imagine a string of blind men each touching each other. The first one does not see, the middle one does not see and neither does the last. The claim of the brahmans is like this. The first one does not see, the middle one does not see and neither does the last. So it seems that the faith of the brahmans turns out to be groundless (M.II,169-70).
The Buddha also rejected the practice of animal sacrifices, the efficacy of rituals and the caste system, all of which are legitimized by the Vedas. Those who say that the Buddha was a Hindu or that Buddhism is a reformed version of Hinduism are seriously misinformed.
Understanding what the Buddha said requires looking at your mind, your motives, feelings and behavior. Understanding the language the Buddha used (turns of phrase, similes, analogies, etc.), the subjects he discussed and how he chose to approach them, requires knowing something about the world he lived in. Take the Vedas, the sacred scriptures of Brahminism. At least some knowledge of the Vedas makes more sense of how and why the Buddha presented some of his teachings the way he did. Vedic Brahmins used to keep three sacred fires burning and worship them. In reference to this the Buddha spoke of the need to extinguish the three fires (i.e. greed, hatred and delusion). A brahman was considered accomplished if he knew (i.e. was able to recite from memory and to explain) the three Vedas.
For the Buddha, a person was spiritually accomplished if he has realized the Three Knowledges (tevijja); arising and passing away of beings according to their kama, and the knowledge of the destruction of the defilements (A.I,165). According to the Vedas, the Brahmins were the apex of humanity because they were born of or created from Brahma's mouth. The Buddha said his enlightened disciples were the apex of humanity because they were ‘born’ of the Buddha's mouth, ‘born of Dhamma, created by Dhamma’ (It.101). And of course the Vedas taught that one could only be a Brahmin by being born of Brahmin parents. For the Buddha, one became a Brahmin by acting the way a Brahmin was supposed to act (tam aham brumi brahmanam, Dhp.397-411).
The Brahmin sages spoke of the blissful, eternal Self (atman. In later Upanasadic thought sat, chit, ananda) while in contradistinction to this the Buddha a taught dukkha, anicca and anatta. These and dozens of other aspects of the Dhamma mirror in one way or another Vedic concepts, the Vedas being the basis of mainstream religious thought during the Buddha's time.
Another important aspect of the Vedas that influenced Buddhism was how they were preserved and passed on. The old canard that critics of Buddhism always raise is that in being orally preserved for several centuries the records we have of the Buddha's teachings must be very reliable, worthless even. In reality, long before Buddha, the Brahmins had evolved ways of remembering and passing on the Vedic hymns with an extraordinary degree of accuracy. Many of the Buddha's disciples were Brahmins and they bought to their new faith the skills they had been schooled in as part of their education, and used them to preserve the Buddha's words. There is an excellent article on Wikipedia called ‘Vedic Chant’ which explains how this was done. The article ‘Vedas’ is very informative too.
Quite apart from all this, at least some familiarity with the Vedas is a good anyway. They are amongst the most beautiful religious literature ever written. If you want to do this I would recommend Wendy Doniger's (she of the new Kama Sutra translation, and numerous other excellent works) The Rig Veda published in Penguin Classics and available in most bookshops. Doniger's translations are readable, clear and not overloaded with notes. Her selection and arrangement (108 hymns altogether) also offers a good introduction to this wonderful literature. All the old favorites are here – The Hymn to the Water, the Gambler's Lament, the Hymn to Creation (Nasadiya), In Praise of Generosity, and my favorite, The Croaking of the Frogs. Some of this must have been familiar to the Buddha and he must have sometimes heard the melodious and hypnotic sound of the Vedas being chanted.
Here are two examples of Vedic chanting: This first one is a slightly modernized rendition of Vedic chanting and the second example is the real thing, done as it was done at the time of the Buddha. Brahmins can do this for hours at a stretch; with perfect intonation and without error.