A language dies only when it is completely forgotten by history.
Even when a language is no longer spoken conversationally, it survives for other purposes. Take LatinLanguage, for example. It even continues to develop.
Unfortunately, there are plenty of languages that have died in such a way. Many of these languages are not written, so when their people die, their language and history die with them. Others just have been supplanted by colonialism and CreoleLanguages.
Also refers to ProgrammingLanguages which are only of historical interest (if any), and have little or no code in current production use. Some languages (much of the original Algols, PL/1, etc.) were actively-used languages at some point in the past, but have fallen into disuse. Most dead languages, though, are those which never made it into production use (and many of which were never intended for production use) - languages designed as part of someone's master's thesis, or otherwise serving some research aim, toy languages, etc. (Note that "production use" here does include active development by the research community; the term means "using the language to solve real problems" rather than "using the language for its own sake", not "used in a business environment".)
See also LegacyLanguage, MainstreamLanguage
A living language is one which changes and grows, just like any other living thing. For natural languages, this usually means it is spoken by young children - they being the architects of language. A language may be used and yet dead.