If someone is described as being "dead to the world," it generally means that he or she has fallen into an extremely deep sleep. This is an English idiom that implies that a sleeping person has no awareness whatsoever of his or her surroundings or of anyone else in the vicinity. The phrase "dead to the world" can also be applied to someone who is not necessarily asleep but is still completely ignorant of everything near him. Its meaning comes from the accepted figurative meaning of the world "dead" as someone who is unaware or numb to stimuli.
When someone uses a word or phrase that has a meaning different than the meaning that might be expected based on the literal definitions of the words, he or she is using an idiom. Idioms are useful in that they allow people to add color and impact to speech that might otherwise be too dull. These phrases get their meanings from how they are used in the culture and understood by the people listening. One such idiomatic expression is the phrase "dead to the world."
This phrase suggests that the person in question has fallen into slumber that is overwhelmingly deep. As a result, this person likely cannot hear anything that is going around him or her, even if the noises are significantly loud. The phrase also implies that the person is missing out on a great deal during this deep sleep. For example, someone might say, "Despite all that happened in this room, he slept through it all, completely dead to the world."
There are certain occasions when someone can be described with this phrase even if he or she is not asleep. Such a person might be awake but still not aware of all that is going on around him or her. This ignorance can mean that people described this way are oblivious to even others who are directly in front of them. As an example, consider the sentence, "I thought that he heard me, but you know that he's dead to the world when he has those headphones on."
"Dead to the world" is one of many idioms that is not meant to be taken literally. Obviously, when someone is described in this way, it does not mean that he or she is literally deceased. Instead, the meaning of "dead" in this phrase is a figurative meaning, more closely associated with someone who is oblivious rather than actually dead.