Syriac is a mostly-extinct language or set of languages. Although rarely used as a full language in its own right, it's still used as a script for religious documents in certain places in the world. Syriac began as a simple dialect, sometime around the 5th century BCE, evolving through many different periods, splitting into various dialects, and eventually moving to the verge of extinction.
The name may also sometimes be used as a blanket term for all of the Eastern Aramaic languages, including Palmyrene Aramaic, Arsacid Aramaic, and Mandaic. More specifically, Syriac is usually used to describe the language spoken in Osrhoene, around Edessa. Old Syriac eventually became the state language in the 2nd century BCE.
Beginning in about the 3rd century, Syriac began to be used as the religious language for Christianity, particularly in the region around Edessa. It was used as a vessel to transport Christianity, and the language was further formalized to aid in producing a Syriac Bible.
Near the end of the 5th century, a large number of Syriac-speaking Christians fled to Persia to avoid persecution by Greek-speaking Christians. This led to a fairly large schism within the Syriac-speaking faith, as well as within the language. Middle Syriac split into what is known as Western Middle Syriac and Eastern Middle Syriac, which have substantial dialect differences, both in pronunciation and vocabulary, although they are still entirely mutually intelligible.
Western Middle Syriac remains the language of the Malankara Syrian Orthodox Church, the Maronite Church, the Mar Thoma Church, the Syriac Orthodox Church, the Syrian Catholic Church, and the Syro-Malankara Catholic Church. Eastern Middle Syriac remains the language of the Assyrian Church of the East, the Chaldeann Catholic Church, the Chaldean Syrian Church, and the Syro-Malabar Church.
The language went into an abrupt decline beginning in the 7th century, as Arabic began to become dominant in the region. In the 13th century, when the Mongols invaded the region, the language fell even further, coming close to becoming fully extinct. Pockets survived, however, and in the modern age it has had a bit of a resurgence.
Modern Syriac has similarities to its Classical and Middle forms, but has absorbed elements of local Aramaic dialects along the way. As a result, Today's dialects have wide differences depending on the region. The most well-known dialect of Modern Western Syriac is Turoyo, which is spoken in Tur Abdin in Turkey. Modern Eastern Syriac is in many ways similar to Eastern Aramaic, a group of Jewish languages.
Aramaic and Assyrian Neo-Aramaic also use the same alphabet, so there's a great deal of literature in Syriac. Perhaps most notably, the Dead Sea Scrolls features writing in the Syriac alphabet.