A classical language is a language with a literature that is classical. According to UC Berkeley linguist George L. Hart, a classical language "should be ancient, it should be an independent tradition that arose mostly on its own, not as an offshoot of another tradition, and it must have a large and extremely rich body of ancient literature."
When we realize that an educated Japanese can hardly frame a single literary sentence without the use of Chinese resources, that to this day Siamese and Burmese and Cambodgian bear the unmistakable imprint of the Sanskrit and Pali that came in with Hindu Buddhism centuries ago, or that whether we argue for or against the teaching of Latin and Greek [in schools,] our argument is sure to be studded with words that have come to us from Rome and Athens, we get some indication of what early Chinese culture and Buddhism, and classical Mediterranean civilization have meant in the world's history. There are just five languages that have had an overwhelming significance as carriers of culture. They are classical Chinese, Sanskrit, Arabic, Greek, and Latin. In comparison with these, even such culturally important languages as Hebrew and French sink into a secondary position.
In this sense, a classical language is a language that has a broad influence over an extended period of time, even after it is no longer a colloquial mother tongue in its original form. If one language uses roots from another language to coin words (in the way that many European languages use Greek and Latin roots to devise new words such as "telephone", etc.), this is an indication that the second language is a classical language.
The following languages are generally taken to have a "classical" stage. Such a stage is limited in time and is considered "classical" if it comes to be regarded as a literary "golden age" retrospectively. Thus, Classical Greek is the language of 5th to 4th century BC Athens and, as such, only a small subset of the varieties of the Greek language as a whole. A "classical" period usually corresponds to a flowering of literature following an "archaic" period, such as Classical Latin succeeding Old Latin, Classical Sumerian succeeding Archaic Sumerian, Classical Sanskrit succeeding Vedic Sanskrit, Classical Persian succeeding Old Persian. This is partly a matter of terminology, and for example Old Chinese is taken to include rather than precede Classical Chinese. In some cases, such as those of Arabic and Tamil, the "classical" stage corresponds to the earliest attested literary variant.