You want to display categories and/or subcategories on archive pages? the shop page? the categories and tags pages?
You can do that via the Theme Customizer.
1- To open the theme customizer, go to your admin dashboard -> Appearance -> Customize
2- A list of all the theme customizer options will appear, navigate to WooCommerce -> Product Catalog
You have 2 main options:
1- SHOP PAGE DISPLAY: as it sounds, this option affects the shop page and you can choose what to display, categories only or products only or both.
2- CATEGORY DISPLAY: this option affects product categories. You have 3 options, show products only, subcategories only or both.