The exchange rate of a currency is its price in terms of another currency. A USD/INR rate of 65 means that the price of $1 is Rs. 65. The RBI publishes daily reference rates for the USD, the Euro, the Japanese Yen, and UK Pound Sterling. However, the USD/INR rate is the most widely tracked exchange rate in India.
The Rs. /$ exchange rate is determined by market forces of demand and supply. Exporters and global investors into India supply dollars; importers and global investors who take money out of India demand dollars. When foreigners invest in India, and we have a good export growth, the rupee appreciates. When we import too much and foreigners sell off their investments in India, we have rupee depreciation.