The Latin Language didn't really die out, it evolved into the various Romance languages--such as Spanish, Portuguese, and French. Somewhat modified forms of Classical Latin persisted among nobility, clergy, and academia from Middle Ages into the 19th century, but these were not spoken as a native language anywhere.

Cultural and geographic factors influenced the development of changes to local dialects, such that the Latin spoken in the former Roman Empire at the dawn of the Middle Ages was notably different from that of Caesar and Augustus. While very common among people across the empire, the aristocracy wouldn't be caught dead speaking what is now called 'Vulgar Latin' in public setting--it would be as jarring as the Queen of England speaking Scouse.

The Appendix Probi, written sometime in the 3rd or 4th centuries, is one of our primary sources for the evolution of the Latin language. Intended as short guide for 'correct' Latin pronunciation, the beginnings of modern Romance languages are plainly visible in its comparisons between 'correct' and 'incorrect' Latin. One example of this found in most modern Romance languages, is the loss of the word initial /h/ in Italian Latin ('corrected' in the Appendix with "Hostiae non ostiae"), such that words like 'Honoris' (Honor) and 'Hominem' (human) were pronounced more like 'Onoris' and 'Ominem.'

While the underlying factors as to why language change occurs remains somewhat mysterious, that the speech of the common masses was changing in different ways across the Roman Empire was never in question. By the early medieval period, varieties of Latin spoken in Hispania were only partially intelligible with the Latin languages of Gaul, Italia, and Moesia, and within a few centuries those dialects would diverge into over two dozen languages.

But as the spoken Latin language was quickly becoming the spoken Latin languages, the written Latin lanuage was hardly changing. Written languages are usually much slower to change than spoken dialects. This is visible today in English, as the spelling of 'knight', 'gnome', 'gnat', and 'knee', did not change when the /kn/ and /gn/ consonant clusters were pronounced simply as 'n'. But in the former Roman Empire, it meant that literate people across Europe could generally understand eachother. Education in Latin persisted among the upper classes through Medieval and Early Modern European history because it served as a useful means for political leaders, clergy and academics, to communicate with other important people halfway across the continent. While Medieval Latin was itself subject to limited regional variation, these differences did not significantly impede communication between leaders of Medieval Europe.

Starting in the Late Middle Ages, an intellectual movement sprung up in Europe calling for increased writing in vernacular languages, though continuing to use the Latin writing system. A few authors began writing primarily in vernacular languages. Dante Alighieri was one of the most prominent figures of this movement, writing his Divine Comedy in Tuscan rather than Medieval Latin. With the advent and spread of the Gutenberg Printing Press in the mid 15th century, the labor cost of transcribing works was massively reduced, making it possible to easily produce large quantities of even niche literature for the first time. Vernacular works began to be published more frequently, and standardized written forms of vernacular languages were formulated across Europe. The Protestant Reformation, which saw churches across Northern Europe reject Ecclesiastical Latin in favor of Vernacular languages, further encouraged the decline of Latin among the upper classes.

While Latin was rarely used for literature by 1650 and increasingly uncommon in European diplomacy, it remained dominant in academia well into the 1700s. Any medicinal student is all too familiar with the Latin anatomical terms coined by researchers writing in Latin in early modern Europe. The 18th century downfall of Latin even in scientific writings resulted in large part from a lethal feedback loop: As fewer works were published in Latin, the usefulness of learning Latin was reduced, reducing the number of people who learned Latin, meaning that fewer works were published in Latin...such that by 1800, Latin was very rare, and by 1900, it was virtually extinct.

The influence that Latin had had in the millenium and a half after the fall of Rome was enormous. Vernacular forms of the language evolved into the Romance languages spoken across much of Europe, as well as most of the New World, and scattered areas of Africa and the islands of the Pacific. But the influence of Latin doesn't end with its Romance language descendents--not all languages using the Latin alphabet are actually descended from Latin.

English serves as an early instance of a non-Romance language adopting the Latin alphabet. Previously written primarily using the Futhorc Script, influence from the Catholic Church led to a gradual shift to a Latin based script around the turn of the Second Millenium. Other Runic scripts of Northern Europe were also replaced by Latin with the spread of Catholicism.

Colonialism saw the suppression and destruction of non-Latin writing systems in the New World by conquistadors and clergymen, such that today, indigenous languages like Nahuatl are still almost exclusively written using Latin based scripts. Other surviving indigenous languages did not have true writing systems in the first place, and subsequently adopted Latin scripts as a result. The Cherokee language is exceptional in that it adopted an entirely original script, which while influenced by Latin is by all means a distinct system, with 85 characters in a syllabary system (one character per syllable) more like that of Japanese than of English. The success of the Cherokee Syllabary would inspire efforts to devise other syllabaries for Native North American languages--most successfully for Inukitut--but these systems were only adopted by a handful of the hundreds of Native American languages, the vast majority of which simply adopted Latin.

As large European colonial efforts spread across Africa, Asia, and Oceania, literacy in the Latin-based colonial languages was encouraged, and often the use of non-Latin based scripts was discouraged or prohibited. The particularly intensive French effort to Latinize the Vietnamese language in the early 1900s led to the rapid extinction of the Chinese-based Vietnamese writing system, and its wholesale replacement with a Latin one. In other cases, previous writing systems did not die out entirely, but still became less common than their Latin replacements--such as the Jawi script of Indonesia, or the use of Arabic script across East Africa. Lacking significant motivating factors to cease the use of Latin following decolonization, Latin Scripts have remained in place in nearly all former European colonies.