Generally, the prompting to close all open programs means any programs you have started from your Programs menu and that appear on your taskbar. For example, if you have Word and Excel open, you would have an icon for each of them on your taskbar. And, yes, these would appear in the Task Manager panel that appears when you hit Ctrl/Alt/Del, along with those programs represented by icons in the system tray (where you see the Norton anti-virus icon).
Closing programs that appear in the tray area, such as Norton Anti-Virus is also a good idea. Anti-virus software, in particular, can sometimes interfere with software installation.