The core idea is to establish autonomous cities that can adopt a stable, development/investment friendly legal, social, and political environment -- by simple copying.
Hong Kong is a SAR (Special Administrative Region) of China and has retained British Common Law.
Romer makes his case better than I can summarize it.
I will point out that it is based on historical proof of concept. Developing countries rapidly adopt technology from developed countries (for example, cell phones). There is no inherent reason that they can't adopt different legal, social, and political institutions that are critical to development.
By early 2011, Romer was working with Honduras to implement his ideas.