This library implements the framework for KDE parts, which are elaborate widgets with a user-interface defined in terms of actions (menu items, toolbar icons). See KParts::Part.
The library also provides a framework for applications that want to use parts. Such applications need to inherit their main window from KParts::MainWindow and provide a so-called shell GUI, which provides a basic skeleton GUI with part-independent functionality/actions.
Some KParts applications won't be specific to a given part, but expect to be able to embed, for instance, all types of viewers out there. For this the basic functionality of any viewer has been implemented in KParts::ReadOnlyPart, which viewer-like parts should inherit from. The same applies to KParts::ReadWritePart, which is for editor-like parts.
You can add actions to an existing KParts app from "outside", defining the code for those actions in a shared library. This mechanism is obviously called plugins, and implemented by KParts::Plugin.
For a complete, and very simple, example of how to use KParts to display any kind of file (i.e. making a generic viewer), see the docu for KParts::ComponentFactory::createPartInstanceFromQuery()