I guess you are talking about people like Eduardo Saverin, who gave up his United States citizenship and moved to Singapore. He did this probably to save money on capital gains taxes. As facebook becomes a publicly traded company, he will have to pay lot of taxes as an American citizen.
Singapore is a bit different, because they do not have capital gain taxes. In light of this, bloomberg.com states that he would save about 67 million dollars by doing this. Of course, Saverin states that he is making this move, because he loves Singapore. This could be true, but it is doubtful.
A few years ago, Jim Rogers did something similar. However, he retained his United States citizenship. For him, it was more of a business move, because he saw more opportunities in Asia than in America. With the growth in Asian markets, people are moving East. China is all the rage these days.
Singapore has become the tiger economy of Asia which means their economy is competitive in the business world. Most business are going moving there because they see a lot of potential from that place.They also saw that it is a popular place for tourist and there is a wide range of different races living there which means it would not be hard to sell their product, for example, if the singaporeans there doesn't like the product they can still sell them to the Indians which they might like. The standard of living in singapore is also high which means that the people there can afford to buy stuff which supports the theory of demand and supply where if people have money then the demand for supply would increase.