You can use an annotated annotation to create a meta-annotation, for example consider this usage of @Transactional in Spring:
/**
* Shortcut and more descriptive "alias" for {@code @Transactional(propagation = Propagation.MANDATORY)}.
*/
@Target({ElementType.METHOD, ElementType.TYPE})
@Retention(RetentionPolicy.RUNTIME)
@Transactional(propagation = Propagation.MANDATORY)
public @interface RequiresExistingTransaction {
}
When you enable Spring to process the @Transactional annotation, it will look for classes and methods that carry @Transactional or any meta-annotation of it (an annotation that is annotated with @Transactional).
Anyway this was just one concrete example how one can make use of an annotated annotation. I guess it’s mostly frameworks like Spring where it makes sense to use them.