When something abates, it diminishes; there is less of it. To abate is to decline; to reduce in strength or vigor.
An abatement is a reduction; it is also a diminishing, a lessening in degree, a moderation.
In law, an abatement is a decrease in the payment a debtor owes to creditors because he does not have the money and assets to pay in full. In the case of someone who is deceased (has died), his/ her estate lacks the money and assets. This must be by mutual agreement or ordered by a judge.
If we say, global financial turmoil has finally abated, we are saying, global financial turmoil (chaos) has become diminished in strength and rigor; it is no longer as intense as it once was.
If we say, investors are hoping that tight credit will abate, we are saying, investors are in the act of hoping that tight credit will loosen; it will no longer be as tight.
If we say, some believe Greece needs to have an abatement, we are saying, some believe Greece requires a reduction in the payments it is expected to make to creditors (including many French and German banks).
Some might feel that the current economic turmoil will not abate until heavily indebted countries receive an abatement of this kind. This is one school of thought.