Wrapping my head around Categories
Craft site has the excellent document How do I list the entries related to a category?

Building on that, you would fetch your category (by slug), and then the entries related to the category.

{# Fetch the category with slug 'categorySlug' #}
{% set category = craft.categories.slug('categorySlug').first() %}

{# Fetch all of the entries related to this category #}
{% set entries = craft.entries.relatedTo(category) %}


Then loop over those entries.