Categories describe what a ticket is about — as opposed to departments, which are about who handles it. Manage them under Configuration → Categories.
Categories power your analytics and saved-view filters. Classifying tickets consistently — for example "Billing question," "Bug," "Feature request" — makes your reports far more useful and lets agents build focused queues of the tickets they care about. A small, well-chosen set of categories works better than a long list nobody applies consistently.