Let's start from a place of thinking about English.

Today, 'English' looks like the language that we are conversing in now.

400 years ago, in Shakespeare's time, 'English' looked and sounded a bit different. Try reading an original language version of. Shakespearean play: it's mostly intelligible, but there are some spellings that aren't used anymore, colloquialisms that don't readily make sense, and even whole words that you'd probably have to loom up.

Go back to Chaucer's Canterbury Tales, some 650 years ago. It's even more difficult to comprehend - not impossible, but not easy.

Now take a look at Beowulf, which was composed roughly 1300-1000 years ago. There's the odd word that looks understandable, but most of it looks like it's in another language. It's not, though: it's in English, and old form of English that we call 'Old English,' and it's the language that would, after 1300 years of evolution in the southeastern portion of the island of Britain, become what we know as English today.

Go back another 700 to 1000 years, and the version of 'English' that we find back then, the most direct ancestor of the language we have today, isn't even called 'OLD English' yet, but rather 'Germanic,' or if you want to narrow things down a bit more, 'North Germanic,' and it's the root language from which English, German, Norse, Danish, Icelandic, and Swedish will all eventually evolve.

Now, imagine that instead of speaking 'North Germanic' 2000 years ago, you're actually speaking living in Rome and speaking Latin. Augustus is alive, Julius Caesar and Cicero both died within the last 50 years or so, and you're speaking and writing a form of Latin that later scholars down to the 21st century will come to call 'Classical Latin.' Scholars and literary elites - both then and now - will consider this form of Latin the 'best version' of Latin and will rigidly teach that exact form of it (along with a slightly derivative later form known as 'Church Latin') to their students for centuries to come, preserving that 'Classical Latin' form for the next 2000 years as a language of culture, learning, and scholarship.

But.... as we've seen, languages evolve. Just as the people of Northern Europe who were speaking 'North Germanic' 2000 years ago are now speaking very evolved, localized derivitive of those languages today (English, Norwegian, Swedish, etc) so too the Latin language that actually gets used day to day in places where Roman Empire used to exist, like France, Italy, Romania, Spain, and so on, now speak a localized, evolved form of Latin that's undergone 2000 years of natural, localized evolution. In Spain, it's Spanish. In France, it's French. And in Italy, it's Italian. There are others. (Romanian is a special, somewhat disputed case.) Collectively, they are known as the 'Romance' languages because they all evolved from the language of the Romans: Latin.

When did Latin get replaced by Italian? It never did. It BECAME Italian, slowly, over 2000 years. Just as 1300 years ago there was a form of English that we now know as 'Old English,' 1300 years ago in Italy there were various dialects and forms of a language that was somewhere between Classical Latin and the Italian we know of today. At various points along that 2000 year timeline scholars and rulers looked around and noticed how far the vernacular language (the spoken language of the street, not the unchanging classical language of scholarship and ritual) had diverged from the 'Classical Latin' of Augustus' day, and jotted that down somewhere for later scholars to read, but that doesn't mean that Latin officially became Italian on that day, or any of the others, just as there's no official date when we can say that 'North Germanic' became English. These evolutions are very gradual, and in a very real sense, English is still North Germanic, just a very evolved and highly localized dialect of it. The same is true of the relationship between Italian and Latin. The people of Italy are STILL speaking Latin... it's just a form of Latin that's undergone 2000 years of evolution.