Sanskrit is an Indian language belonging to the Indo-Aryan family of languages, having a history of about 3500 years.
The earliest records in Sanskrit language are found in rigveda which is dates to about 1500 BCE. The oldest surviving book on Sanskrit grammar is written by Panini in 4th century BCE. All the vedas, upanishads, and Indian epics like Ramayana and Mahabharata are written in Sanskrit along with several other works of poetry, drama, science, philosophy and religion.
In the current day, it is one of the scheduled languages of the Indian constitution. While the language is not widely spoken anymore, within India and worldwide, there is an undercurrent of revival of the language in academic circles and in the general population. Sanskrit is the language of many Hindu and Buddhist scriptures and is used to the current day for religious purposes in these religions. The status of Sanskrit in the Indian subcontinent is akin to that of Latin in the western world.
The Wikipedia article on Sanskrit is a treasure-trove of information.