First of all, I would like to explain to you what offshore exactly refers to. Offshore is an international term meaning not only out of your country (jurisdiction) but out of the tax reach of your country of residence or citizenship.
The main reason people usually invest offshore is to avoid paying tax.
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.
A very important thing to consider, when investing offshore, is the political stability of the country. Basically, what can happen to you is to lose 100% of your money, while trying to avoid paying 40% in tax. However, fact is that today, over half of world's transactions take place offshore. Investments grow much faster offshore, because the gain on investment, that is reinvested is much larger, since not tax was paid on the gain.
Due to the recent Organization for Economic Cooperation and Development (OECD) and European Union regulations, many jurisdictions that have a dependence on Great Britain have decreased or eliminated their privacy laws. The offshore tax havens that have independence from Great Britain have retained their strong privacy laws. Many of these countries receive a majority of their income from offshore services so they have a financial incentive to keep the privacy laws in place on a long-term basis.