Adobe Experience Manager (AEM) content fragments are created and managed as page-independent assets.
They allow you to create channel-neutral content, together with (possibly channel-specific) variations. You can then use these fragments, and their variations, when authoring your content pages.
The full functionality of Content Fragment Management is not available in classic UI. See Page Authoring with Content Fragments in the standard authoring documentation.
The Content Fragment component can be seen in the classic UI sidekick, but further functions are not available.