What does these box sign mean?

that is ambiguous checkbox state. in this case it means that every category contains few subcategories. if all subcategories are false, parent category will be false. if all subcategories are true - parent will be true. and if few subcategories are true, and few are false, so parent category will be in this state.

What does this box sign mean?

They are not checked or unchecked.

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