Death of an organism.

Depends on the proximate cause of death.

Disease can linger in the body for years before causing death. An infection can cause death in a matter of days, or even hours. Running head-on into a cement mixer truck or a freight train is pretty much an instantaneous 'event'.

 

So it stands to reason that death is an event in which electrical activity of brain permanently ceases...but I am no expert so I may be wrong.

 

It is cells that die, which lead to the death of the organism. Obviously, in complex organisms, which cells die, and how many determine the fate of the organism.
The topic of death is also a philosophical one. Consider "grafting", where trees have their limbs removed and grafted onto other trees, commonly done with cultivated fruit trees. In a sense, the parent tree never dies.

 

The medical definition is the cessation of all vital functions. To that I might add the word "irreversible". This in fact is not easily determined so a common legal definition for human death is brain death as indicated on an electroencephalogram (EEG). However, the EEG is not a perfect instrument and in some countries patients or their families are allowed to choose from a set of legal criteria which includes a "do not resuscitate" instruction in the case of a cardiac arrest. So the technology may exist to restore vital functions, but may not be applied even in the absence of documented brain death.

In a complex organism, the organism itself may be irreversibly "dead" but some organs are still "alive" and can continue to be capable of functioning for a while. This is why we can transplant vital organs.

http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2598255/

EDIT: Note even mitochondria can be transplanted.

http://www.ncbi.nlm.nih.gov/pubmed/23080556