Offshore banking is banking services that are licensed and governed under the law of the land where the bank is providing the services. Unlike some restriction you may find in the banks in your country you may not see the same limitation at an offshore bank. Contrary to people misconception about foreign banking as something illegal, the offshore banking options are legal, and if you open an offshore account to diversify your investment portfolio by seeking bank account in countries where you see more growth of your funds and investment, it is in your legal right to open the offshore bank account.
However is offshore banks are taken as a means to launder money or to do tax evasion, this will be treated as a criminal offense and the law of the land will penalize any such person or entity who are running illegal offshore accounts.