According to Investopedia, "stock acquisition non-open market" means that shares are either bought or sold directly to and from a company. These transactions are strictly private.
Non-market stock transactions can be initiated by either party. For example, most transactions occur when an options investor holds the right to purchase a stock privately at a preset price but can sell that stock on a public exchange. Companies can also introduce a tender offer in which shares are repurchased back from shareholder. Nonetheless, Investopedia notes that every transaction must be filed with the U.S. Securities and Exchange Commission. Investors involved in these transactions are called "insiders." The form needed to file with the SEC when completing a non-open market transaction is Form 4. These insiders are usually employees, directors and officers but can also be individuals. This is commonly confused with insider trading or the purchase or sale of a security based off nonpublic information regarding the security. This in turn creates an unfair advantage, since all investors do not have the same access and their confidence is undermined. Some economists, such as Milton Friedman, believe that insider trading benefits the economy, while other experts believe it reduces economic growth due to the cost of capital.