The 'check and fix categories' located in the menu Catalog > Tools as well as in the category interface (Catalog > Categories) is used to check specific information on categories within the database.
On a technical point of view, the option recalculate the nleft and nright of each category, to eventually fix the category tree.
It's strongly recommended to apply this option when you rework the category tree, especially when dragging/dropping to re-organize the order of your category.
Once the option is open, click on the icon on the toolbar:
Once the status goes green, you can refresh your Sc interface with F5.