In Joomla! a Category is a collection of Articles. It is the middle level in the hierarchy Sections -> Categories -> Articles. For example, a website might have Sections called "Animals" and "Plants". Within the "Animals" Section, the website might have Categories such as "Birds" and "Mammals". Within the "Birds" Category, the website might have Articles such as "Parrots" and "Sparrows".
Categories are maintained using the Category Manager (help screen) which can be reached in the Administrator (Back-end) by clicking on the Content menu, then the Category Manager menu item.