Administrators can check or uncheck the store level setting to display Immediate Categories whose product's Names are there on Search Result Page.  

When the value of “Display Subcategory Products In Parent Category” is checked on the Store level in the Admin application and there is at least one product result is available for a keyword that is searched on the webstore then the list of all those hyperlinked categories names whose products are available above the facets section will be displayed in an accordion on the search result page.

When the value of “Display Subcategory Products In Parent Category ” is unchecked on the Store level in the Admin application and there is at least one product result available for a keyword that is searched on the webstore then the list of all those hyperlinked categories names whose products  (that are directly associated) are available above the facets section will be displayed in an accordion on the search result page.

Ex 1: Consider Hardware is the parent category and Chain and Rope, Doorknobs and Locks are the child categories, in this scenario considerations will be as follows:

Hardware = P1 

Chain and Rope = C1 

Doorknobs = C2 

Locks = C3 

Any Products added under C1, C2 or C3 will be visible under P1

Ex 2: Consider Tools  is the parent category and Power Tools is the child category of tools and Drills  is the Child Category of power tools and Cordless is the Child Category of drills, in this scenario considerations will be as follows:

Tools = P1

Power Tools = C1

Drills = C11

Cordless = C111 

Any products added under C111 will be visible under C11, C1 as well as P1

Any products added under C11 will be visible under C1 and P1

Any products added under C1 will be visible under P1

Notes - 

1. The sequence in which the categories are displayed will depend on the display order of categories in the Store’s catalog. 
2. Users are redirected to the respective category page if they click on any category name.