This button is disabled while PA-RUN is running a program. When enabled, clicking this button has the same effect as clicking on the main window's Close button in the top right corner: It closes the PA-RUN application.
However, when the PA-RUN Tray Icon is visible and the option "Close to Tray" is active then PA-RUN is not closed but is always minimized to the Tray Icon. You can override this behavior by pressing the CONTROL key while clicking the Close button: In this case PA-RUN is being really closed (and not just minimized to the Tray Icon).