Calling Latin dead language is a matter of semantics. There are those who would suggest Latin is not dead, that it lives on in everyday language used by billions of people across the globe. Others argue that because there are routine updates to Latin published by the Roman Catholic Church, it is still alive and developing.
However, Latin is no longer used, on a daily basis, by the vast majority of people outside of specific religious settings, where tradition dictates its use. It is no longer anyone's native language. While its use is still taught, Latin is no longer considered to be a developing language to the degree of most modern languages.
The reasons for Latin dying out are numerous. Perhaps the most significant one has to do with the decline of the Roman Empire. During the Roman time period, language was standardized to a greater extent. Just as learning English is vital to those living in the United States today, to really succeed during the Roman times, one needed to learn Latin.
Because Rome was the most powerful political entity in the western world at the time, most of those who had any ambition to thrive within its vast system had a desire to learn Latin. As a result, the language spread rapidly. However, that rapid expansion would eventually begin to plateau and finally decline.
Latin continued to be used during the Medieval time period. Throughout Europe, it remained the language of choice. However, with nothing to unite the continent, there was no need for a uniform language. So slowly, over a period of hundreds of years, Latin began to change as different regions developed their own dialects and idiosyncrasies.
Eventually, these dialects would become unique enough to be named their own languages. Today, we know them as the Romance languages. The most commonly spoken and recognizable of these related languages are: Spanish, Portuguese, Italian and French. Romansh, a little-spoken language used in a very small part of Switzerland, may be the modern language that most closely resembles classical Latin.
Though not directly related to the Romance languages, Latin still has had an effect on many other languages. English, for example, which is not one of the Romance languages but a Germanic one, can trace nearly two-thirds of its words back to Latin roots. In addition to the Roman Catholic Church, Latin is also used in the science and mathematic communities extensively.