What is Brain Death?

Legal Definition
Brain death is the complete and irreversible loss of brain function (including involuntary activity necessary to sustain life). Brain death is used as an indicator of legal death in many jurisdictions, but it is defined inconsistently. Various parts of the brain may keep living when others die, and the term "brain death" has been used to refer to various combinations. For example, although a major medical dictionary says that "brain death" is synonymous with "cerebral death" (death of the cerebrum), the US National Library of Medicine Medical Subject Headings (MeSH) system defines brain death as including the brainstem. The distinctions can be important because, for example, in someone with a dead cerebrum but a living brainstem, the heartbeat and ventilation can continue unaided, whereas in whole-brain death (which includes brain stem death), only life support equipment would keep those functions going. Patients classified as brain-dead can have their organs surgically removed for organ donation.
-- Wikipedia
Legal Definition
Brain death is the complete and irreversible loss of brain function (including involuntary activity necessary to sustain life). Brain death is one of the two ways of determination of death, according to the Uniform Determination of Death Act of the United States (the other way of determining death being "irreversible cessation of circulatory and respiratory functions"). It differs from persistent vegetative state, in which the person is alive and some autonomic functions remain.

Brain death is used as an indicator of legal death in many jurisdictions, but it is defined inconsistently. Various parts of the brain may keep living when others die, and the term "brain death" has been used to refer to various combinations. For example, although a major medical dictionary says that "brain death" is synonymous with "cerebral death" (death of the cerebrum), the US National Library of Medicine Medical Subject Headings (MeSH) system defines brain death as including the brainstem. The distinctions can be important because, for example, in someone with a dead cerebrum but a living brainstem, the heartbeat and ventilation can continue unaided, whereas in whole-brain death (which includes brain stem death), only life support equipment would keep those functions going. Patients classified as brain-dead can have their organs surgically removed for organ donation.
-- Wikipedia
Legal Definition
This applies to the state of a brain that shows no electrical activity.