By this I assume you mean the period from roughly 1500 BCE, which signals the end of the Indus Valley Civilization, until the rise of the Gupta Empire in the 4rd-6th centuries CE. This is a span of time that covers roughly 2000 years and contains some of the most important formative moments in Hindu history.
First, the Vedas were developed in the period 1500BCE-800BCE. These collections of hymns and mythology were intended to accompany complex rituals. The brahman priests performed these rituals, chanting the Vedas to the gods, thus maintaining the cosmic harmony.
But the Vedic rituals were complex, expensive, and difficult. Commentaries on the Vedas began to teach that one should worship the gods within, through meditation, fasting, and prayer. The Upanishads mark this change in orientation. These texts taught that one's true Self, the immortal atman, was divine in nature and that through yoga and meditation one could lose oneself in divine union.
A third major religious movement developed in this period in Hinduism. Many of these teachings (of Vedic rituals, of sacrifice, of losing oneself in God) were often reserved for upper classes and/or people who left society on a spiritual quest. But in the period 200BCE-200CE the great epics, the Ramayana and the Mahabharata presented many of these ideas in a popular format with stories of heroes. In particular, the Bhagavad-Gita that all people should act selflessly, performing their caste duties, and live in virtuous devotion to God. So this third movement may be described as a popular movement, a way of making these earlier teachings more publicly available.
By the way, it used to be thought that India was subject to invasions by people called the Aryans. In recent decades, this idea has been largely abandoned. Although a few scholars current in the field still believe the Indus Valley Civilization fell to some Aryan invasion, there is little evidence to substantiate this idea.