You can choose in which order your categories appear in the catalog by setting the position number. The closer the position number is to 1, the closer to the top of the catalog page the category will appear.
Navigate to the category you want to change the order for under Content > Organize > Categories and Edit.
In the Details section, reorder the categories by changing the Position field, then Save the changes.
If you have a Featured Category, or the user has a Favorites category, then the number 1 category will appear right after those two. When you have a Featured Category selected for the slider, that category will not appear among other categories since it's already displayed in the slider. For example, if you have a fitness site and you choose cardio as your Featured Category, regardless of the position it was in before, it will be the first to stand out, and it will not be present anywhere else in the catalog.
For instance, you can observe that the category "Taking Care of the Garden" is on the Featured Category banner and doesn't appear in the listing above.