The visibility controls are part of view layers, designed to help organizing what you want to see or work on.
View layers reference to collections, and allow to set their visibility, selectability and other options. A view layer can have any collection enabled, and multiple view layers can use the same or different collections.
Each view layer can be rendered separately as individual Render Layers to help composite your scene.
You can edit the current view layer collections in the Outliner.
There you can enable and disable collections, hide them temporarily, globally, among other options.
Read more about Collections in the Outliner.