Bear with me for a moment, as some history is necessary to understand how Latin spread and survived prior to the transition. As Rome transitioned from monarchy to republic in the middle of the first millennium BC, Latin was just one—and not even a particularly important one—of the profusion of languages spoken in the Italian peninsula. Other communities spoke related languages like Faliscan, Oscan, and Umbrian, all of which belonged to the Italic branch of Indo-European language family. The Greek colonies in the south of Italy spoke, naturally enough, Greek, which belongs to another branch of the broader Indo-European family. The Etruscans, at that point the dominant cultural and economic power in Italy, lived in northern Italy and spoke a totally unrelated language.

As the Romans expanded first throughout Italy and then beyond, Latin went with them. Language followed empire, swamping its Italic relatives within Italy, and Etruscan, too, before spreading throughout Europe. Greek proved more stubborn, but it too declined in importance. In Gaul, Spain, North Africa, the Balkans, Dacia (today’s Romania) and parts of Britain, Latin coexisted with and then eventually displaced an array of native languages.

Latin mostly sank its roots in the western half of the Roman Empire. It was never a static language, or a homogeneous one. Speakers could distinguish educated, high-status Latin from that of common people. There were words and phrases that speakers associated with particular regions of the Empire. We do the same thing in American English, with the regional differences between hero and hoagie, tennis shoes and sneakers, or soda versus pop versus coke. There were regional accents, too: Latin speakers were aware that people from North Africa, for example, had a distinctive way of pronouncing vowels. Over time, just as English has today, Latin changed.

While the Roman Empire was still a going concern, though, the various regional accents and varieties of Latin never diverged all that much. Why? Constant movement. What defined the Roman Empire relative to the periods before and after was the mass transfer of goods and people from one region to another. North African grain fed the enormous population of Rome; olive oil from Spain and wine from Gaul supplied the troops on the Rhine frontier. Soldiers from the Balkans served in Britain and along the Danube. Merchants from Italy did business in Carthage, Tarragona, and Marseille.

In linguistic terms, this created a situation of constant “dialect leveling.” As speakers of different varieties of the same language come into contact, which they often did in the Roman world, the differences between those varieties tended to drop off. Sufficient movement of people over a long-enough time frame served to prevent the formation of distinctive dialects, and eventually languages.

To get to your actual question, when the Roman Empire fell apart in the fourth, fifth, and sixth centuries, that easy mass movement of goods and people slowly but surely came to an end. The unifying state institutions that had bound the Roman world together—the army and the tax system—no longer drove transfers of soldiers and grain over long distances. With far fewer people moving, the process of dialect leveling, what had kept Latin relatively homogeneous, also slipped away. Over the course of centuries, the Romance languages began to diverge from the homogeneous Latin standard of the Roman Empire.

The problem is that it’s not easy to see this process happening. As with English today, the written standard of Latin—the baseline, “correct” way of writing the language instilled by teachers over the course of centuries—had an enormous influence on the texts we see. Even if the way they were speaking the language was changing dramatically in the sixth, seventh, and eighth centuries, the written language wasn’t changing that much.

It’s only in the ninth century that we begin to see stirrings of a Romance language that was markedly different from Latin. Educational reforms under the Holy Roman Emperor Charlemagne helped to create an awareness of the difference between how folks were speaking and how they were writing. We see the first unequivocally Romance text, in the form of the Strasbourg Oaths, around the middle of the ninth century. Even then, though, it’s centuries more before evidence of divergent Roman languages—French vs. Catalan vs. Castilian vs. Venetian vs. Tuscan—truly starts to emerge.