What are the Unreferenced checkboxes mean and why are there three options?

The checkboxes that you see everywhere in the system are the "Unreferenced" box. If the box is checked, then the object it's referring to is unreferenced, and could possibly be deleted.

However there are special checkboxes for 3 of the objects : Scripts, Layouts and TableOccurrences. For these it's not a checkbox, but a calculated graphic that shows the Unreferenced status in in one of 3 ways :

Referenced - empty.
Unreferenced but may be in use - shows a dash inside a box.
Unreferenced - checked.

Unreferenced but may be in use.

The "maybe" state is for a script or layout that is unreferenced, but still appears in the menu, and so it might still be in use by the users, even though you never see it referred to.

For a TO the maybe state is for a TO that has nothing referring to it, but has more than 1 relationship off it. In that case, it's possible to have a GTRR or a calculation that starts at one of the other related TO's and goes via this unreferenced one to the second TO. This would mean that the TO is required as an intermediary step in the relationship.

But also there is a maybe "dash" shown when the object is unreferenced, but the file is using Indirection to reference these types of objects. For more information about Indirection there is a separate FAQ page available.

So to be able to do a search for these TOs/scripts/layouts, when you click on the field in either mode, you get a pull-down instead of a checkbox. The values for the pull-down list are

0 - Referenced
1 - Maybe Unreferenced
2 - Unreferenced

That way you can still search on the field, but you also get a very clear instant response from the checkbox graphic.