Often, the system tray / notification area icons near the system clock are there as a convenience to quickly launch utilities or customize their behavior via their context menu (right-clicking on the icon). Those icons can generally be hidden, so that they don't take too much space. In other cases, however, the tray icon is used to notify us of a possibly important status change. For antivirus and other security software, that information can be crucial.
To configure which icons are visible, which are hidden, and when, click on the arrow button next to the clock and other status icons, and click on the Customize link as shown on the screenshot. Windows 7 will open the "Notification Area Icons" screen in the Control Panel, with a list of a list of program icons for most installed programs, and recently run applications.
Next to each application name and icon is a dropdown menu, whose choices are the same for all programs. Here are the three options, and an explanation:
1) Show icon and notifications: icon always visible next to the clock.
2) Hide icon and notifications: icon and messages always hidden.
3) Only show notifications: icon hidden until program wants to communicate.
For antivirus software and anti-malware only use options 1 or 3 ("show icon", or at least "only show notifications"). Ideally, always show the icon to immediately know of a change in status. Some apps' icons are very "chatty", but those communication settings can often be configured through the program's options.
In addition to program icons, there are "System Icons": these are Windows icons that include internet connection strength, volume level (speaker icon), warnings about security (flag icon), and power management (plug and battery icon). On a laptop, for example, you'd want to see your connectivity and battery life icons, but don't necessarily need to see the volume icon. To customize these, click on "Turn system icons on or off" at the bottom of that window.