What is Bank Secrecy?

Legal Definition
Bank secrecy (or bank privacy) is a legal requirement in some jurisdictions which prohibits banks providing to authorities personal and account information about their customers, except in certain conditions, such as if a criminal complaint has been filed. In some cases, additional privacy is provided to beneficial owners through the use of numbered bank accounts or in other ways. Bank secrecy is prevalent in certain countries such as Switzerland, Lebanon, Singapore and Luxembourg, as well as offshore banks and other tax havens under voluntary or statutory privacy provisions.

Numbered bank accounts were first created in Switzerland by the Swiss Banking Act of 1934, where the principle of bank secrecy continues to be considered one of the main aspects of private banking. Switzerland has also been accused by NGOs and governments of being one of the main instruments of the underground economy and organized crime, in particular following the class action suit against the Vatican Bank in the 1990s, the Clearstream scandal and the terrorist attacks of September 11, 2001. Former bank employees from banks in Switzerland (UBS, Julius Baer) and Liechtenstein (LGT Group) have testified that their former institutions helped clients evade billions of dollars in taxes by routing money through offshore havens in the Caribbean and Switzerland. One of these, Rudolf M. Elmer, wrote, "It is a global problem...Offshore tax evasion is the biggest theft among societies and neighbor states in this world." The Swiss Parliament ratified on June 17, 2010 an agreement between the Swiss and the United States governments allowing UBS to transmit to the US authorities information concerning 4,450 American clients of UBS suspected of tax evasion.

Advances in financial cryptography (e.g. public-key cryptography) could make it possible to use anonymous electronic money and anonymous digital bearer certificates for financial privacy and anonymous Internet banking, given enabling institutions (e.g. issuers of such certificates and digital cash) and secure computer systems.
-- Wikipedia
Legal Definition
The bank's promise to keep financial affairs and dealings of the customer confidential. This doesn't apply to credit information that is shared freely. Certain information mst also be made available due to antiterrorist legislation.