COMPLETING THE BANKING UNION
"A single banking system is the mirror image of a single money. As the vast majority of money is bank deposits, money can only be truly single if confidence in the safety of bank deposits is the same irrespective of the Member State in which a bank operates. This requires single bank supervision, single bank resolution and single deposit insurance."
Source: Five Presidents' Report "Completing Europe's Economic and Monetary Union", 22 June 2015
Commission explanation of the need for banking union, and its structure here