Buddhist Hybrid Sanskrit is a category used to describe a number of related languages used to record Buddhist scripture in northern India. BHS, as it is commonly referred to as, is an Indo-European language, in the same branch as classical and modern Sanskrit, Pali and the other Prakrit languages, and many of the modern languages of the Indian subcontinent (e.g. Hindi, Bengali, and Sinhala). Chronologically, BHS is classified as a middle Indo European language, appearing in the same general epoch as Pali and most of the other Prakrit tongues.
More significantly, BHS appears shortly after classical Sanskrit began to become the language of choice for literature and religion in India. While religious texts had always been preserved in Sanskrit since the advent of the Vedic religion, there were always literary and religious works being preserved in other, popular languages as well. After Panini codified and popularized Sanskrit, other literature began to be re-written and translated into Sanskrit, to bring it into line with the tastes of the time and the new mania for Sanskrit literature.
Buddhist literature, for instance, had long been preserved in a variety of Prakrit tongues- Sanskrit-based languages that were actually used as spoken languages in the various regions of India, and which provided the precursors to the modern Indian languages. Since the Buddha had not taught in Sanskrit himself, and had rejected the idea of translating his teachings into Vedic Sanskrit, Buddhist texts had proliferated in a variety of local languages. Some, like Pali, eventually themselves became codified and regularized in response to their long-term use as the language of the preservation of a religious canon.
Following the rise of Sanskrit to dominance throughout India, these Prakrit texts began to be back-translated using the carefully defined grammar of Panini's Sanskrit. In most cases, the more extensive and contemporary Prakrit vocabulary was used instead of the Sanskrit terms. Additionally, these newly translated texts often modified or deviated from the rules of strict Sanskrit grammar, combining innovations from the Prakrit languages, or otherwise just introducing grammatical errors.
In effect, these efforts to make Buddhist scriptures conform to Sanskrit standards created a whole new class of language- languages used almost exclusively in religious texts, like Sanskrit, and using much (but not all) of the standard Sanskrit grammar, but with significant divergences in certain areas of vocabulary and grammar. Regional variation played a significant role in these variations.
Furthermore, the language was again expanded and altered after Buddhism spread outside of India. New back-translations were created- in this case, texts in local languages (such as Chinese) being translated into Sanskrit in order to lend them greater authority. The most well known example of this phenomenon is the Awakening of Faith in Mahayana, usually attributed to Ashvaghosa. New errors and innovations appeared, and these texts- which often were not recognized as having initially been non-Sanskrit works- propagated them back to the larger Buddhist community.
Buddhist Hybrid Sanskrit continues to be studied, much like classical Sanskrit and Pali. It was used in recording many Mahayana sutras, the Prakrit originals of which have often since disappeared. In some cases, BHS versions preserve documents that are no longer extant in their original language. In other cases, it is the BHS version that is missing, having been translated into Chinese or a Central Asian language, and the original existing only in fragments, or in quotations in other sources.
As a hybrid form of classical Sanskrit and the later Prakrits, knowledge of Sanskrit is quite useful in learning BHS. However, it is often studied separately after learning regular Sanskrit, because there is such a difference in vocabulary, and because there are so many irregular variations. Institutions that teach Sanskrit or Pali are likely to teach Buddhist Hybrid Sanskrit as well.