Once you stop breathing, or the heart stops beating, the body is unable to provide oxygen to your cells or remove carbon dioxide. The lack the oxygen and build up of carbon dioxide and other toxins leads to rapid cell death. You can be brain dead and still keep other parts of the body "alive" as long as the body is able to circulate fresh blood and remove carbon dioxide and other toxins. That's why death is usually defined as cessation of circulorespiratory function. About how fast various cells die, from the following site:

https://www.sciencefocus.com/the-human-body/when-we-die-does-our-whole-body-die-at-the-same-time/

>The brain and nerve cells require a constant supply of oxygen and will die within a few minutes, once you stop breathing. The next to go will be the heart, followed by the liver, then the kidneys and pancreas, which can last for about an hour. Skin, tendons, heart valves and corneas will still be alive after a day. White blood cells, which are more independent, can keep going for almost three days.

In recent years there has been a move in the medical profession to define death earlier than was the norm, based on brain death or early symptoms of brain death because as u/theangryfurlong says the organs can be kept 'alive' after brain death, making transplanting them into another person's body more practical. If death is defined by permanent cessation of heart function there is very little time for organ transplants.

Individual cells die when they lose their ability to carry out aerobic metabolism because ATP is needed to maintain membrane integrity. Accordingly, the brain is one of the first things to die, some of the tissues that take longer include hair and fingernails, which can live for several days active the heart has stopped and the brain is dead.

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