Your Joomla Article Category Module allows you to display the articles in a specific Category.
This Module is very similar to your Article Categories Module so when setting this up you need to pay attention to two similar words:
It is very easy to get confused between the two words above - sometimes even we at UsingJoomla.com get it wrong - as in we do not get what we 'wanted' - try one way, see the result - if the result is not what you wanted create the Module "the other way".
When you want to try something such as a new Module, set the access level to 'Super User', publish the Module on a specific page of your website, and then login to the frontend of your website, navigate to the page where you published the Module (in this case) and you will see the Module but no-one else will see it.
If / when you are happy, set the access level to, for example 'Public' where everyone will see it.
Below we present an image showing an Articles Category Module - used as a Module on this Article page. The Module is displayed on the right-hand side when viewing on a large screen, or below the article content when viewed on a small screen (for example on a mobile phone.
In Joomla, Modules are created and managed via the Administrator area.
Site Modules - Articles - Category
Modules - Options