Latin was the original language of Rome, and as a result of its incredible expansion, it became one of the official languages of the Roman Empire. The other language was Greek, which to the Romans was the language of culture and refinement; in fact many upper class Romans spoke Greek better than they did Latin.
Latin became the dominant language in the western part of the Empire, as well as the eastern province of Dacia, so that over 1500 years after the fall of Rome, its influence can still be felt in Italian, Spanish and French and even in English and Romanian. Most of the words in these languages can trace their roots back to Latin, and anyone who speaks one of the Romance languages can easily understand a lot of Latin. Similarly, any speaker of Italian, French or Spanish can understand a lot of the other languages in this group without any formal training, simply because of their shared Latin core. Therefore Latin is a useful linguistic bridge between modern languages.
Not that Latin is a dead language. It continued to be a vibrant language of the Church and of science for over a thousand years after the end of the Roman Empire. Renaissance scholars and even scientists and philosophers of the 17th century continued to publish their books in Latin, knowing that in this way they would be understood by colleagues throughout Europe because Latin remained essentially a universal language. It is only in modern times that Latin has fallen somewhat by the wayside, and has been replaced by English as a lingua franca. However even now it is a living language, and dictionaries have been published which update Latin with modern words for things such as computers and cellphones. The Catholic Church continues to publish a website in Latin and to occasionally holds religious ceremonies in the language.
It must be understood that even during Roman times, Latin was not a static language and it evolved over time and in different regions. There was the formal Latin of the learned upper classes and then there was the vulgar Latin of the lower classes and in the remote parts of the empire. In the end, it was the vulgar tongue, which survived and adapted when the Empire was swamped by invaders. Our modern languages trace their roots primarily to the Latin of the common people, and not the language of the poets or great writers.
Knowing even some Latin is useful and a great way to sound really sophisticated and knowledgeable even when you atre talking about something inane and commonplace.
If you are interested in learning more about Latin, we have posted here a useful grammar and text to teach you the basics. Another good way to learn Latin is on Duolingo, which offers an easy and free course that will teach you the basics of grammar and vocabulary. You will be surprised how many words in Latin will be already familiar to you.
Failure and Grandeur of Roman Civilization