Latin was the language spoken by the ancient Romans. (Rome was in the district called Latium in Latin, and 'Latin' originally meant simply 'from Latium'.) The Romans famously had the greatest empire in Europe over at least the first four centuries of the Common Era.
The Latin language is of great importance in several ways. Historically, the language of the Roman Empire was obviously important, and it was then associated with the Christian religion which developed within, and eventually became the only official religion of, the Empire.
Throughout Europe, it was the language of Higher Education from the time of the Roman Empire until about the 18th century; and the language of scholarship even later than that. With Greek, it was one of the two Classical Languages, because they possessed the two most admired literatures - the classics.
It was also the language of the Christian religion in Western Europe until the Reformation in the 16th century. The old form of Western European Christianity (the Roman Catholic church) only stopped using Latin as the language of church services in the 1960s, under the Second Vatican Council. (Latin is still the official language in the Vatican, the Pope's state within the city of Rome.) These two circumstances of its use (education and religion) made the language hugely important for 2000 years. Its high status as the language of the Universities and the learned professions, particularly Law and Medicine, helps to explain why so much Latin can be seen in academic writing. (See Abbreviations - Academic, (Latin).)
Its importance in etymology is also high. Vulgar Latin, the ordinary everyday language actually spoke by Romans as opposed to the formal literary language in which they wrote, is the origin of many modern languages. These are called the Romance languages, from the name 'Rome'. It has also contributed greatly to the vocabulary of English - both directly, because of its historical use in religion and education, and indirectly, in words taken from various Romance languages, expecially French, as a result of the Norman Conquest. For more on the importance of Latin in the history of our English Language, see Latin in the History of English.
You may like to see how to pronounce Latin Words and Phrases in English.