Latin is an Indo-European language of the Italic branch, formerly spoken by the Romans; the Romance languages that survive today emerged from the evolution of its vulgar version.
The Roman Empire guaranteed the maintenance of Latin in its classical version; with the fall of the Roman Empire, the language of the streets accelerated its evolution and moved into the stage we call Vulgar Latin, which continued to change until it formed today’s Romance languages.
On the other hand, Classical Latin remained the language of culture in Europe for many centuries. Most European languages, especially the Romance languages and English, have incorporated a great deal of vocabulary directly from Classical Latin, particularly for technical terms.
Latin also remained the liturgical language of the Catholic Church until the Second Vatican Council; today there are no native speakers of Latin, but it is the official language of the Vatican State, where it is studied and used. It is incorrect to say that Latin is a dead language, because it has not become extinct, but has rather evolved into other languages.