The plural term Vedas has two related meanings in Hinduism. First, it refers to the four Veda texts: the Rig Veda, the Yajur Veda, the Sama Veda and the Atharva Veda. Second, "Vedas" may also to the literature of the Vedic period which are based upon the four Vedas; the term thus includes the Brahmanas, which are commentaries on each Veda, and the Upanishads, which are philosophical treatises based upon them. Sometimes the term may also include the Sutras, books which are rules and regulation codified according to different schools, even though these texts were written later in the period of Classical Hinduism.
The Vedas proper were composed and then transmitted orally beginning around 1400 bce and probably recorded in writing about 1000. The first three Vedas are collections of material for sacrifices. The Rig Veda contains 1028 hymns to the various gods (Indra, Agni, Soma, Rudra, etc.) which a priest recited loudly during a sacrifice to attract the god's attention to it. Many of the Rig Veda's verses are mantras, vocalizations that encapsulate and resound the nature of Brahman. The Yajur Veda contains mantras and other instructions for the priest(s) who actually perform the sacrifice. And the Sama Veda adapts mantras and verses from the Rig Veda to music which is then sung during the sacrifice. The Atharva Veda differs from the first three in that it does not relate to sacrifice and also contains spells and magic rites.
The contents of the Vedas should make it clear that these are texts for the Brahmins. It is this varna who monopolized the Vedas and used them as the basis for education, requiring students to memorize large amounts of them. Until quick recently, it was forbidden for anyone not of the Twice-born castes even to hear the Vedas recited.
The Vedas (including the Brahmanas and Upanishads) constitute the sacred texts of Hinduism. Hinduism considers these texts to be sruti, a word which means "heard." The Vedas were written down by rishis (holy men who are the mythical founders of Hinduism) who "heard" them during deep meditation. Thus, the texts come neither from gods nor men, but from the nature of the cosmos itself.
The Brahmanas were composed between 1000 and 700 bce as commentaries on the four Vedas. As such, each Brahmana is attached to a specific Veda. As commentaries, they explicate matters needing explanation. For example, they discuss the meaning of mantras, specify how to perform certain sacrificial actions only briefly mentioned, and describe the impact the sacrifices have on the eternal world. In short, they function as a manual teaching the proper use of the material in the Veda to which it belongs.
The Upanishads are as different and diverse as the Vedas to which they belong. Composed between roughly 700 and 300 bce, delve into discussions of the deep inner meaning of their respective Vedas. Thus, discussion can range from the meaning of the sacrificial altar as the center of the world to the priestly singer's role and the meter he sings in. If there is anything that unifies the Upanishads, it is their continual discussion of atman, Brahman and their relationship--a theme which becomes important in Classical Hinduism. For a passage translated from the Upanishads, go here.
This literature is revered but is not considered holy in the same way as the Vedas. They are termed smriti, i.e., "remembered." This means that they are traditional and originally passed on orally. They have a human rather than a divine origin.
Sutra has two meanings: a short pithy saying (like a proverb), and a collection of such sayings. The Sutras, as the latter, then are a collection of the former. In this way they organize many of the ideas of the Vedas into a series of rules and regulations than can be practiced. The Sutras came at the end of the Vedic literature and each one is usually derived from a Veda and its commentary literature. One of the most famous sutras in the West is that rulebook of sexual pleasure, the Kama Sutra.
The Mahabharata centers on the five Pandava brothers, who are sons of a king whose kingdom lies on the southern slopes of the Himalayas. In a fit of passion, the eldest brother gambles away the kingdom and his brothers in a dice game. The rest of the story is about the struggles and battles of the brothers to gain back their kingdom. The greatest warrior of the five brothers is Arjuna. On the night before a major battle, he has doubts about the rightness of killing the enemy, who are his cousins. At that point, his charioteer, Krishna (who is an avatar of Vishnu), engages him in a discussion about performing one's duty (dharma), and about the paths to a better life, namely, devotion (bhakti yoga), action (karma yoga), and knowledge (jnana yoga), with an emphasis on Karma Yoga. This discussion is known as the Bhagavad Gita and it forms the basis of much popular Hinduism, including strengthening worship (bhakti) and devotion. For some passages translated from the Bhagavad Gita, go here.
The Ramayana, composed around 200 bce, is the story of Rama and his wife Sita. Rama is heir apparent to his father, the King of Ayodhya. He learns of the beautiful, royal Sita of a neighboring kingdom and wins her hand in marriage by performing the mighty feat of stringing Shiva's bow. Due to palace intrigue at home, however, Rama is sent into exile as a sadhu for 14 years. Sita, ever faithful, chooses to accompany him. They have many adventures, the greatest of which happens when Sita is kidnapped by the demon king Ravana, who disappears with her to his kingdom of Lanka (=Sri Lanka). Rama enlists the help of the monkeys, especially their champion Hanuman. Hanuman finds Sita, and enlisting the assistance of a monkey army, helps Rama regain Sita. During her captivity, Sita spurned all Ravana's advances, quoting the Vedas and lecturing him on dharma. Rama is ultimately returned to his kingship in Ayodhya, but the people doubt Sita's faithfullness, since she was a captive for more than a year. In the end, she called upon the earth goddess to bear witness and she is swallowed up forever.
Each of the main figures of the story represent an ideal type in Bhakti. Rama is the strong, active, hero, while Sita is the faithful, loyal, beautiful wife. Once it is realized that Rama is the incarnation of Vishnu and Sita is the incarnation of his consort Lakshmi, then Hanuman becomes the representation of an ideal follower, one who is totally devoted to the god.
If the Vedic literature was composed by and for the use of the Brahmin caste and thus remained an elite and esoteric literature, then the Puranas and their stories were designed for and used by the average Hindu. The eighteen major Puranas are collections of stories about the gods and their activities. The earliest were composed around 400 ce, but others, especially some minor ones, were created a millennium later. Thus the Puranas span the period from Classical Hinduism into Medieval Hinduism. They tend to emphasize two points: bhakti (devotion to a god) and dharma (doing one's personal and social duty). The Puranas thus fall into three groups: those dealing with the stories of Brahma, those concerning Vishnu (and his avatars and consort(s)), and those about Shiva and the goddesses associated with him.