When should we use Vue.js's component

When I study the feature of Vue.js's component system. I feel confused when and where should we use this? In Vue.js's doc they said

Vue.js allows you to treat extended Vue subclasses as reusable components that are conceptually similar to Web Components, without requiring any polyfills.

But based on their example it doesn't clear to me how does it help to reuse. I even think it complex the logic flow.