Thank you @blanchsb. I’ve found a decription in the Blender 2.82 manual: It’s the Global Viewport Visibility icon and it serves – if I’m understanding it right – to switch off or on the viewport visibility of an object in all files where it’s instanced:
“This will still render the object/collection, but it will be ignored by all the viewports. Often used for collections with high-poly objects that need to be instanced in other files.”
So, our eyball icon can be described as “Local Viewport Visibiliy icon” that switches on or off the viewport visibility of an object only in the file that you’re currently working on.
