User invisibility can be good for privacy in your network (website). This is a User Group setting that you are in full control of. If you want to allow your users to choose to be invisible on your site, you would set it for each user group that you want to allow to do this. 

Follow this guide for this setting for this to work.

• In the AdminCP, Click Members and go to Usergroup settings. Select User from the Apps drop-down list and select the UserGroup that you want to allow users to enable the invisibility(in this case, we selected Registered Users)
  

• After setting Apps=User and Groups=(your selected Usergroup), scroll down to see the option Can select to be invisible? Set to Yes to Enable
  

• Scroll down and look for the setting If enabled, members of this user group will be able to hide from the Browse section when they enable "Invisible Mode" from Profile -> Privacy Settings Set to Yes to Enable
  

• Click SAVE Changes and Clear Cache after making changes.