There are 3 types of Component Operators, or COMPs, and each have different uses:
Object components create, light, and view 3D scenes
Panel components create UI components such as buttons, sliders, and window panes
Other components include components that create keyframe animations, replicate other Operators, and create output windows
Component Operators are generally used in conjunction with other Operators. The 'Object' components are used in various combinations to create and render SOPs and 3D scenes. The 'Panel' components are used to create UIs and various containers to create output rasters. The 'Other' components are used for various tasks, such as keyframe animations, dynamic Operator replication, opening windows on various displays, etc.
An interesting fact to put things in perspective is that a large amount of TouchDesigner is made from components inside of TouchDesigner. Understanding this really helps in grasping the granularity of TouchDesigner, and how to approach working on various projects. For example, all Panel components are made of other Operators. Create a Button COMP, and inside its Network, its background is made of a Text TOP, and its on/off values are being generated by a Panel CHOP. Similarly, all of TouchDesigner's UI is made and stored in the 'ui' container in the root of all projects. Even the menus and dialogs, like the MIDI Mapper Dialog and the Variables Dialog, are created using other TouchDesigner components.