Bank is clean money that you earn by upgrading Mansion Map Buildings, collecting the Martial Art Studio's Daily Bonus, defeating Neutral Gangs on the Street Map, and completing certain Achievements, Targets, and Daily Tasks.  You can also turn your Cash into Bank through money laundering at the Accounting Firm.  Bank is used for expanding your City, buying special Item chances in the Night Club, and it's also necessary for upgrading certain Technologies.