This option lets you configure your object list columns in a fast and convenient way. If you use it, all currently selected attributes in the attribute list are shown as columns in the object list:
You could also configure the object list columns by normal menus: The according options are accessible by choosing View - Column Field Chooser.
By the way: If you see the Use Attribute as List Column option disabled and gray, then your current application focus is not in the attribute list or your LEX is maybe in Read Only mode.
Here is another convenient way to specify an attribute to be shown in the object list as a column: In the attribute list, just mark the attribute(s) you want to be displayed as a column in the object list, open the context menu (right mouse-click) and choose the option Use Attribute as List Column.