What exactly does "exact" and "broad" mean in keywords adwords tool?

What exactly does "exact" and "broad" mean in keywords adwords tool?

I have read several articles on this, but still fail to understand.
For example I have the following keywords in adwords:
Cheese in NY - Volume: 22.000 searches
Cheese NY - Volume 22.000 searches
and
[Cheese in NY] - Volume: 100 searches
[Cheese NY] - Volume: 90 searches
Why the big difference?
As far as I understand [keyword] does not mean its actually typed in in quotes.
So if only 100 people use Cheese in NY, where do the other 21k searches come from?