Show depending on another field

First, the "Value" field needs to contain actual values, not the name of a field. If the categories field holds the category's id, then you would place integers (comma-separate) like 14,16,17 - which in this example would cause the field to display when the categories field is set to either of these three categories.

Second, you may be misunderstanding the purpose of this field. The behavior of this "showon" feature is to show or hide a field based upon the value of some other field. It does not load the values of one field in reponse to the value of another field. In other words, it will not provide the behavior of filtering articles based upon which category is set on the categories field. (Attaining behavior like that will require javascript and possibly AJAX, as the change of the value in the field categories occurs within the browser and is not detectable by the server. This behavior is available as a filter on the list view. To add this type of filtering on the single-item form, you will need to code it after you generate the component with Component Creator.)