Functional interfaces are used in Java 8 for a variety of purposes, including:

• Declaring anonymous functions: Functional interfaces can be used to declare anonymous functions, which are functions that are not defined in a separate named method. Anonymous functions can be used in a variety of places, such as in lambda expressions and method references.
• Implementing interfaces with a single abstract method: Functional interfaces can be used to implement interfaces with a single abstract method. This makes it easier to implement interfaces and to write code that is more modular and reusable.
• Passing functions as arguments: Functional interfaces can be passed as arguments to methods. This allows you to pass a function to a method without having to create a separate object to represent the function.
• Referencing methods: Functional interfaces can be used to reference methods. This allows you to use a method as if it were a function.

Here are some examples of how functional interfaces are used in Java 8:

• The Runnable interface is a functional interface that declares a single abstract method, run(). The run() method is executed when the Runnable object is executed.
• The Comparator interface is a functional interface that declares two abstract methods, compare() and equals(). The compare() method compares two objects and returns an integer indicating their relative order. The equals() method compares two objects and returns a boolean value indicating whether the objects are equal.
• The Predicate interface is a functional interface that declares a single abstract method, test(). The test() method takes an object as its input and returns a boolean value indicating whether the object satisfies the predicate.