What does it mean when someone is brain dead?

Answer 1

brains produce measurable levels of electrical activity in specific patterns. If the brain is no longer working it no longer produces electrical activity in pattern and is considered "dead", as in no longer capable of thought.

Answer 2

When someone is brain dead, it means there is no activity going on at all in the brain and it will never come back. Other parts of the body might still be working, but the brain is essentially dead, hence the term.