Latin has been the official and commonly used language in the Ancient Rome and its provinces, in Latin Empire, and, partially in the Holy Roman Empire. Over the centuries, it became (and still remains) the official language of the Roman Catholic Church and the Vatican.
As the Romans continued the Greek tradition of sciences and have created the modern approach to the law and medicine, Latin is still used in medicine, law, and other sciences. Speaking some Latin, as well as understanding the Latin culture, especially the Roman Empire, is a must for a well-educated person.
Romans have developed and preserved the classic culture, which started from the Greek sculpture, architecture, philosophy, ways of life and more. This is what has laid the foundation to the modern Western culture the way we know it today. Knowing Latin opens the doors to the Western culture - ancient, medieval and modern.