WIkipedia has a lot to say on the definition of death.
Historically, attempts to define the exact moment of a human's death have been subjective, or imprecise. Death was once defined as the cessation of heartbeat (cardiac arrest) and of breathing, but the development of CPR and prompt defibrillation have rendered that definition inadequate because breathing and heartbeat can sometimes be restarted. This type of death where circulatory and respiratory arrest happens is known as the circulatory definition of death (DCDD). Proponents of the DCDD believe that this definition is reasonable because a person with permanent loss of circulatory and respiratory function should be considered dead.[14] Critics of this definition state that while cessation of these functions may be permanent, it does not mean the situation is not irreversible, because if CPR was applied, the person could be revived.[14] Thus, the arguments for and against the DCDD boil down to a matter of defining the actual words "permanent" and "irreversible," which further complicates the challenge of defining death. Furthermore, events which were causally linked to death in the past no longer kill in all circumstances; without a functioning heart or lungs, life can sometimes be sustained with a combination of life support devices, organ transplants and artificial pacemakers.
Today, where a definition of the moment of death is required, doctors and coroners usually turn to "brain death" or "biological death" to define a person as being dead; people are considered dead when the electrical activity in their brain ceases. It is presumed that an end of electrical activity indicates the end of consciousness. Suspension of consciousness must be permanent, and not transient, as occurs during certain sleep stages, and especially a coma. In the case of sleep, EEGs can easily tell the difference.
The category of "brain death" is seen as problematic by some scholars. For instance, Dr. Franklin Miller, senior faculty member at the Department of Bioethics, National Institutes of Health, notes: "By the late 1990s... the equation of brain death with death of the human being was increasingly challenged by scholars, based on evidence regarding the array of biological functioning displayed by patients correctly diagnosed as having this condition who were maintained on mechanical ventilation for substantial periods of time. These patients maintained the ability to sustain circulation and respiration, control temperature, excrete wastes, heal wounds, fight infections and, most dramatically, to gestate fetuses (in the case of pregnant "brain-dead" women)."[15]
en.wikipedia.org/wiki/Death