The phrase "financial openness" refers to an individual country's approach to foreign investments in corporations within its jurisdiction, to the policies of each country with respect to regulating exports of specified goods and services, and to each government's policy on what is called "capital flows."
Almost all countries maintain some level of control over the amount of wealth that can be transferred abroad (e.g., requirements that citizens declare, upon leaving their country for any period of time, whether they are transporting a certain amount of cash), the types of investments, corporate mergers and acquisitions that can be carried out by foreign commercial or governmental entities (e.g., regulations that require prospective foreign purchases of American businesses that involve the transfer of militarily or commercially-sensitive technologies or "know-how"), and the level of control foreign businesses or governments can exercise over a country's financial institutions. Basically, the fewer such regulations or restrictions, the more "open" the country in question.
Controls on the movement of goods, services, and wealth are considered vital to most countries' ability to secure their economies and people from foreign threats that could develop as a result of certain types of foreign acquisitions, mergers, or investments. An example might be mandatory reviews by U.S. government agencies of proposed Chinese acquisitions of American companies that develop technologies which could be exploited for military or intelligence purposes. In the case of the United States, an intergovernmental organization known as the Committee on Foreign Investment in the United States (CFIUS) reviews such proposed business deals to minimize the prospects of whether foreign governments, that may not be on the best of terms with the United States, acquire American technologies which could threaten U.S. interests. As recently as this week, the French government suggested that it would impose controls on any foreign investment in French corporate and government efforts of developing artificial intelligence technologies and at protecting the personal data of French citizens, which might otherwise be transferred to foreign governments, if openness to foreign investments were allowed.
Financial openness frequently, as mentioned above, refers to the movement of money across borders without government interference. Such capital flows are a very sensitive topic, as governments which want foreign investment in their own financial sectors may not be as open to a reciprocal arrangement that involves capital leaving the country. Such arrangements, however, are often the product of agreements or treaties between governments which share similar ideas on economic growth, as well as on the role of trade and investment in facilitating growth.