The shortest questions are the hardest ones to answer, eh?

A language becomes dormant when it is no longer spoken as the first or primary language of any living person. It becomes extinct when there are no complete records of that language's use and rules.

If I were going to give you a short and concise answer as to why that happens to a language, I'd say economics and culture. It's a hell of a lot more complicated than that, and I'm not necessarily talking about military conquest (though that can happen, too). Language is closely tied to culture, and if one culture swamps another culture, that second culture's language will be under pressure.

The Expanded Graded Intergenerational Disruption Scale was developed as an objective measure of the health of a language by assessing how that language is used. There are 13 steps on this scale, which ranges from Level 0: International (it's known and used between nations in trade and international policy) to Level 10: Extinct (no one uses this language, and no one defines their ethnic identity from the language).

According to the latest edition of Ethnologue, there are 7,106 known living languages in the world. Of these, 21 percent are in the "threatened" or "shifting" levels of the EGIDS scale. This means "intergenerational transmission is in the process of being broken, but the child-bearing generation can still use the language."

Another 13 percent are classified as "dying" languages. No one of child-bearing age is teaching these languages to their children.

The 7,106 known living languages also include 373 "extinct" languages that have disappeared since 1950. These languages no longer hold even symbolic value for the communities that used to use them.

That answers your second question, so let's now tackle your first question. In Alaska, (my subject matter), there are at least 20 distinct indigenous languages. Only Central Yup'ik (spoken in Southwest Alaska) and Siberian Yupik (spoken in Russia and on St. Lawrence Island) are still spoken as first languages in the home. All of them are at at least some risk, and most of them are dying fast. The last fluent speaker of Eyak died in 2008. The last fluent speaker of Holikachuk will die this decade. By 2050, we expect at least half of Alaska's Native languages to have no fluent speakers.

Why is this happening?

The best summation I've seen comes from a paper by Michael Krauss of the Alaska Native Language Center. He published it in 2001 after delivering it as the keynote address at a conference in Kyoto, Japan. Krauss is (in my view) the King of Alaska Native Language Studies, and though this paper is somewhat dated (the number of languages it identifies is off, for example), he two main reasons: number of speakers and socio-economic reasons.

If you have a language spoken by 1,000,000 people, it isn't going to disappear, even if a significant fraction of those people are conquered and forced to use a different language. Size protects you from rapid swings. You can talk to your neighbors in a language, even if the man in a town on the other side of the country needs to talk to you in a different language for commerce.

As Krauss writes: "For relatively small numbers of speakers to maintain their languages indefinitely, certain minimal conditions would bе required, e.g. а viable literacy, and social conditions favorable enough to support or at least tolerate maintenance of that language. The only languages qualifying as realistically "safe" under those conditions, I believe, would bе those that enjoy recognition and support as national languages of nationstates or at least as regional languages thereof."

Now, why are socio-economic reasons so important? Simply put: Trade is survival. Unless you are a hunter-gatherer, you need to be able to trade with someone in order to get the necessities you need to survive. Unless you gather your own food, build your own shelter and mate with yourself, you're going to need to communicate with other people. As the world has become more reliant on long-distance trade networks, the need to communicate over long distances has grown.

With long-distance communication comes more pressure on languages. Take television and radio, for example. When your language isn't appearing in either medium, you have less reason to use it. Krauss once called television "cultural nerve gas," and I see no reason to doubt him.

It's sort of a misnomer to say that Latin "died". All languages are changing and evolving. When you say Latin, I assume you're referring to classical Latin, the Latin taught in schools and which makes up the language of Cicero, Caesar, et cetera. That language was spread out through the Roman empire, and different areas started developing their own unique dialects. At the same time that we had classical Latin, there was also Vulgar Latin, the language spoken by the "illiterate majority" (Coleman 181). As Vulgar Latin spread, it "must have acquired the dialectical variations from which the Romance languages emerged".

Coleman goes on: "The conservative traditions of the schools of grammar and rhetoric did not entirely immunise classical usage against vulgar infiltration. However, they did ensure that by the ninth century AD written Latin and the diverse spoken forms of Latin had ceased to be registers of one language...Caesar and Livy would have recognised the Latin of Nithard's Historiae as a form of their own language; they would have found his citations of the Strassburg oaths as baffling in the romana lingua as in the teudisca." (According to this site, romana lingua refers to the French dialect, whereas teudisca refers to what was spoken in what is now Germany.)

So if you want to place a marker where Latin had fully diverged into extant languages that were no longer mutually understandable with the parent language, the 9th century AD would be a decent date, according to Coleman. The biggest thing to take from this, however, is that in this context languages do not die out as much as they change into different languages. Of course, if you look at the other responses to this question, there is a different sense of language death, when a language has no more speakers.

Source: Aside from the website I cited to clear up terminology, I referenced R.G.G. Coleman's chapter on Latin and the Italic Languages from The World's Major Languages.

On top of what the alaskan wrote I want to add that language has to be understood as an integral part of the culture of an etnicity. In many countries, nationalistic ideals promotes the idea of a nation state, which means that all people in the country should belong to the same culture/etnicity. To achive that, many countries pracitice assimilation processes, which among other things involves denying people their languages. For example by not allowing kids to speak it in school, preventing media from communicating in that language, etc.

These assimilation techniques with the goal of exterminating a culture has been and is stil widely practiced. My country, Sweden did if for a long time against the sami minority. Australia did it against the aboriginals, Turkey is stil doing it against the Kurds, etc.

From a perspective that you can see today, Look at the Welsh language trying to remain dominant in Wales. Although the Welsh language isn't dead, it's declining. Mainly because of outside factors, such as English spoken media, English dominant internet and websites etc...

So what kills a language? the larger more dominant culture spreading via migration, media and the internet.

Also, Historically, outright banning of a language has happened. This is a large factor in the Welsh language's decline too, When England subjugated Wales, you couldn't be a government official if you spoke Welsh, you couldn't speak Welsh at school or at work. It was literally only able to survive because of people speaking the language in their own homes.

http://www.bbc.co.uk/wales/history/sites/themes/society/language_tudors.shtml

1. Languages naturally change over time. That's why Old English is unintelligible to modern English speakers, and why King James and Shakespearean English sound strange to modern English speakers. In the case of classical Latin, the modern descendants of Latin aren't called "Latin" anymore. The colloquial versions of Latin spoken in different parts of the Roman Empire have diverged into different languages, including French, Spanish, Italian, Portuguese, Romanian, Provencal, and Catalan. So Latin didn't really die, it just changed like all languages do, and it hasn't kept the same name it had thousands of years ago the way other languages, like English, Greek, and Chinese have.

2. Sometimes a language really does "die" in the sense that it is replaced by completely different languages instead of changing naturally over time. This tends to happen when the speakers of the language either die completely or when they adopt another language or languages. Sometimes all the people belonging to a particular group simply die out and their language dies with them. One example of this are the Beothuk people of Newfoundland, and many other indigenous American groups who were killed by European disease epidemics or genocide. Other times people abandon their original language in favor of other languages. This is what happened in the British Isles, where people who spoke various Celtic languages (i.e. Cornish, Welsh, Scots and Irish Gaelic) abandoned their ancestral languages in favor of English. In those cases there may be pressure to speak the more dominant language of a ruling class. Parents may encourage their children to speak the dominant language. Kids may learn the dominant language in school, or in other institutions like the military or at work. They may fail to pass the ancestral language on to their kids.

When all first-knowledge persons who knew the language die, the language is generally seen as extinct. There are various definitions and steps; Latin is seen as a dead language although it is widely spoken as a secondary and historical and scholarly language. It is simply not used culturally and indigenously anymore, or to a very small undocumented degree.

In the case of Latin, it didn't really "die", it evolved away. People speaking Latin accumulated enough changes in their local dialects that they could no longer understand each other (or speakers of "standard" Latin, to the extent that there still were any of those). So what was Latin became French, Spanish, Italian, etc. (Also, I should point out since you mentioned it that Latin still isn't 100% unspoken because the Catholic Church and particularly Vatican City still speak it.)

In the case of most dead languages, everyone speaking a native language also speaks some other language which is usually more widely spoken (Native Americans speaking English, for example), and eventually over generations the population speaks the new language exclusively and the old language not at all. Sometimes this is just because the new language is more "useful"; often it's because the new language is spoken by conquerors that forced the population to speak it at some point (as, again, in the case of Native Americans speaking English)

Here is a sample of David Crystal's book Language Death. You may find it interesting.

Lack of social institutions, economic support and cultural enthusiasm

The way a language goes extinct is very much like how a species goes extinct in biology: it fails to reproduce. In the case of language, it means that if it stops being transmitted from the older generation to the next (because of being replaced by a much larger language, most of the time) then it becomes moribund and dies. Most of the time efforts to revive it have mixed results. At best a dead language can be preserved in writing and there will be people who understand it (like Latin). If nobody understands it (except maybe a handful of linguists and archaeologists) then it's extinct, ie. there is no chance of it coming back.

On the other hand, a successful language can evolve into a different one, or split into several new ones, again much like species in biology. Often what happens is a language spoken by a lot of people over a wide area starts to fragment into dialects, which then become distinct enough that they become different languages. This is what happened to Latin.