In the Western Mediterranean at the peak of the Roman Empire, Latin was the overriding language for imperial administration, legislation and military use. It was also the language of the educated elite, used by writers like Cicero, Catullus and Horace. It was also the language of culture, used by poets like Virgil and Ovid, philosophers like Stoics and Plautus and even scholars and doctors such as Frontinus and Hyginus.
Of course, the Romans were a diverse lot and there were plenty of other languages in circulation. There were, for example, the surviving Etruscan dialects of Oscan and Faliscan. And there were also the indigenous languages of Italy, such as Umbrian and Otranto. Some of these dialects even influenced the early development of Latin.
By the second century AD, however, Latin had become so established that it started to develop its own 'dialects' across the empire. These were regional variations in the way the language was pronounced, and they were influenced by a number of things including external influences from other countries, communities and empires.
It’s likely that many Romans were fluent in Greek as well. This was particularly true of the educated elite. It’s possible that, like Victoria, aristocratic children would learn Greek from their nannies as well as Latin. And as they grew older, the language of their education, literature, poetry and science would be Greek. This was a very important part of what it meant to be a Roman.