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 "Special", publish the module on a specific page of your website, and then log-in to the front-end 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.