Yes, it was the language of ancient Rome ! It kind of died out as a language after Rome collapsed but many scholars used it a lot in their writings for many years after. It's still seen on money and all kinds of things. You see it all over on buildings and such in Europe.
Yes it was a real language of course! Latin was used by the ancient Romans during throughout ancient and medieval times. However traces of Latin can still be seen today. For example many of the words we use today have Latin origin.
It was also used for medical terms as well. So when you see certain medical terms, look them up to get the origin, and derivatives, and you'll find that some are from Latin which is now a "dead" language used over 2000 years ago.