An `InheritedWidget` is a special type of widget in Flutter that can be used to propagate data down the widget tree to its descendants. It is designed to optimize the performance of Flutter apps by minimizing the need to rebuild widgets unnecessarily.

An `InheritedWidget` is essentially a widget that contains data that can be accessed by its descendants. When a widget is updated, Flutter first checks to see if any of the widget's ancestors are `InheritedWidgets`. If it finds one, it checks whether the data contained by the `InheritedWidget` has changed. If the data has changed, Flutter rebuilds the widgets below the `InheritedWidget` automatically.

The `InheritedWidget` is used by creating a new subclass of the `InheritedWidget` class, overriding its `updateShouldNotify` method, and then wrapping the widgets that need access to the data with the `InheritedWidget` using its `of` method. By doing this, the descendants of the `InheritedWidget` can access its data directly, without the need for passing the data down manually through each widget.

An example use case of `InheritedWidget` could be a localization widget that provides translated strings to all of its descendants. Since the localization data is unlikely to change frequently, it can be passed down to all descendants using `InheritedWidget`, avoiding unnecessary rebuilds of widgets that have not changed.