Here's a breakdown:
* Latin was the official language of the Roman Empire: The Romans conquered and ruled over a massive area, which included much of Europe, North Africa, and the Middle East. Latin became the language of administration, law, commerce, and military.
* Vulgar Latin emerged: Over time, regional variations of Latin developed, known as "Vulgar Latin." These dialects were spoken by ordinary people and differed from the standardized Classical Latin used in literature and formal settings.
* Romance languages evolved: Vulgar Latin eventually evolved into the Romance languages, such as French, Spanish, Italian, Portuguese, Romanian, Catalan, and others. These languages still share many similarities with Latin in vocabulary, grammar, and syntax.
Therefore, although there was no single "country" that exclusively spoke Latin, the Roman Empire, with its extensive territory and lasting influence, is the closest example we have. Latin was the dominant language of the Roman Empire, and its legacy lives on in the Romance languages spoken today.