Some investors are outside the jurisdiction of high-tax areas, either because they live elsewhere, or because they are temporarily non-resident for work reasons. Such investors can often avoid having to pay taxes on their investments, whether on or offshore, but that is due to the investor's circumstances, not the location of the investment.
So why might an offshore investment be superior to an onshore investment?
The first answer is because it is less regulated, and the behavior of the offshore investment provider, whether he be a banker, fund manager, trustee or stock-broker, is freer than it could be in a more regulated environment.