When NATIVE is selected, this means that the internet connection details of the native Operating System are used.
In Windows this is usually the same as the "Internet" settings configured through Windows Control Panel, or through Internet Explorer's options menu.
In this setting, HANA Studio will utilise whatever proxy server you have configured for internet access.
When DIRECT is selected, any proxy settings are controlled from within HANA Studio and any Operating System settings are ignored.
This is the reason that SAP say to select DIRECT whenever you experience connectivity issues.
Are there any performance benefits from DIRECT? maybe. Since the HANA Studio doesn't need to query for any proxy server settings in the Windows registry, it's possible that the initial connection could be established quicker. Once connected it probably doesn't make any performance improvement over NATIVE.