Categories
Categories are used for product grouping. Each product can be a member of multiple categories.
Also, categories can be configured to appear in the application navigation / menu.
Create a category
Navigate to Catalog → Categories, click on "Show category tree", pick a parent category from the list and click on "Add subcategory".
Tip
If no categories exist yet, when clicking on Catalog → Categories, you'll be automatically presented to the new category form. There's no need for opening the category tree in that case.

Active
This determines if the category should be visible in the frontend store.
Visible in navigation
This determines if the category should be visible in the application navigation / menu.
Adding and removing images
Same rules apply as in products, mentioned here.
Adding products to a category
Click on the "Browse products". A dialog will be shown.

Find the products you want by filtering and sorting the list. Select the products by clicking on the checkboxes on the left of each row and click on "Confirm selection" to complete the process.
Important
You need to save the category to complete adding the selected products to the category.
Click on "Save category" to complete the process.
Category tree

To edit a category, click on it to select it and then click on "Edit category". Parent categories can be expanded to reveal children by clicking on the symbol left to the parent's name.
To delete a category, click on it to select it and then click on "Delete category". A confirmation dialog will appear, and you must confirm it to complete the process.
To add a subcategory, click on any category to select it and then click on "Add subcategory".
Categories can be reordered using drag & drop. After reordering, click on "Save category positions" to save the changes.