Consistency checking allows detecting potential mistakes that can occur when creating a multi-language site, that you will discover as inconsistencies of its elements.
An element has self inconsistencies when one of its fields is not consistent in the context of the element. For example, an article in English language whose category is in Spanish language.
An element has translation inconsistencies when one of its fields is not consistent with respect to the fields of the source of the translation in the 'Reference Language'. For example, an article in Spanish language whose category is not the translation into Spanish of the category of the article source of the translation in the 'Reference Language' (in this case English).
In the below screen capture you can see an example of inconsistencies detected when creating a new menu item.
Note: the screenshot below belongs to KMFasTrans version 3.2.0.