Stealth settings let you to appear online to some people and offline to others. The offline setting is called "Invisible," and contacts will see the little face next to your name as grey. Even though you will appear offline, you can still send and receive messages as normal.
This is useful if you just want to get alerts but not use instant messaging. You can also appear as Invisible to specific contacts or groups of contacts – for example, you may want to appear offline to friends while you're at work, but show that you're online to co-workers.
To always show your status as Invisible:
If you are already signed in and want to switch to Invisible mode for this session:
Note: When you are Invisible to everyone, your Messenger List will appear in italics.
You can appear as Invisible to only specific people:
You can appear as Invisible to only a specific group of contacts: