Sanskrit is an ancient language belonging to the Indo-European family, a family that includes the vast majority of European languages, the slavic languages, the farsi language (the language of Iran) and a good number of Indian languages (excluding the South Indian languages which belong to other linguistic families).
Functioning as the pan-indian cultural language for more than 1500 years, Sanskrit, from the linguistic point of view, is peculiar in the fact that it is not a natural language (such as Latin and Greek for example, also ancient languages belonging to the same Indo-European family). Instead, it’s the product of centuries of grammatical enquiry into the language attested in the Vedas (this one a natural language, or rather, seen its great number of variations, a set of languages strictly related among themselves), the Vedas being a collection of sacred texts belonging to a period ranging approximately from the XV to the VI century BC (the Vedas represent the most ancient corpus we possess into an Indo-European language).
In other words Sanskrit is a grammatical language, which means that it is not a language based on a specific community of speakers, but a language based on the respect of its grammatical rules: while in a natural language the grammar (if it exists at all) describes in grammatical terms the reality of the language (spoken if it’s a living language, written if it’s a dead language), and therefore it can be said that the grammar follows the language, changing when the language changes, with Sanskrit the relation language-grammar turns the other way round, both from a chronological point of view and from a point of view of importance.
Classical Sanskrit spread and established itself as the language of culture and power after that its grammar had been defined in all particulars, in terms of pronunciation, sentence grammar, formation and meaning of the words: that is why it remained unchanged throughout the centuries and everywhere it spread (other than in the South Asian subcontinent Sanskrit was adopted by the Hindu Kingdoms of South East Asia).
The authorities for classical Sanskrit have always been the grammar on the one hand and on the other the models offered by the greatest poets and writers who established the canons for good writing: while Sanskrit grammar is always the same, the various literary genres differ significantly as far as style and syntax are concerned (the vocabulary on the other hand is common to all genres).
The power of expression of Sanskrit, when compared to other languages, depends mainly on the fact that in it every aspect of the linguistic expression is strictly regulated, especially its phonologic, morphologic, semantic and grammatical dimensions, factors that in a natural language are very much culturally and historically determined, if not spontaneous and unconscious.
Sanskrit is a powerful tool for a clear articulation of thought and expression because it imposes to the writers, with its grammatical rules, a careful reflection on the structure of sentences and on the choice of terms, a reflection that, at least in part, can be reconstructed by the readers because it is based purely on the respect of the grammatical rules.
It can be said that Sanskrit is a language that tries to minimize the irrational and unconscious sides of linguistic expression, and that is why it worked very well, over more than a millennium, as a pan-indian cultural language, used to codify and transmit all knowledge (from poetry to science, so to say) and playing a central role in the constitution of an unitarian Indian cultural identity (it is important to keep in mind that ancient India did not have a political unity, so that Sanskrit did not impose itself with military means, as Latin for example did in Europe, but it spread because of its prestige and linguistic power, being itself one of the main factor granting a cultural unity to the sub-continent).