When you password protect a category, the category page, its sub-categories and all the posts within are protected with the same password(s). People must enter a correct password to access any of this protected content.
Each category can have one or more passwords and you can protect as many categories as you like within your website, while leaving others public.
You can either add a single password which will apply to the category and all its posts and sub-categories; or you can set different passwords for each category - for example, if you need to provide a separate hidden category for each person.