What are functional interfaces used for in Java 8?

As others have said, a functional interface is an interface which exposes one method. It may have more than one method, but all of the others must have a default implementation. The reason it's called a "functional interface" is because it effectively acts as a function. Since you can pass interfaces as parameters, it means that functions are now "first-class citizens" like in functional programming languages. This has many benefits, and you'll see them quite a lot when using the Stream API. Of course, lambda expressions are the main obvious use for them.

@FunctionalInterface annotation is useful for compilation time checking of your code. You cannot have more than one method besides static, default and abstract methods that override methods in Object in your @FunctionalInterface or any other interface used as a functional interface.

But you can use lambdas without this annotation as well as you can override methods without @Override annotation.

From docs

a functional interface has exactly one abstract method. Since default methods have an implementation, they are not abstract. If an interface declares an abstract method overriding one of the public methods of java.lang.Object, that also does not count toward the interface's abstract method count since any implementation of the interface will have an implementation from java.lang.Object or elsewhere

This can be used in lambda expression:

public interface Foo {
  public void doSomething();
}

This cannot be used in lambda expression:

public interface Foo {
  public void doSomething();
  public void doSomethingElse();
}

But this will give compilation error:

@FunctionalInterface
public interface Foo {
  public void doSomething();
  public void doSomethingElse();
}

Invalid '@FunctionalInterface' annotation; Foo is not a functional interface

The documentation makes indeed a difference between the purpose

An informative annotation type used to indicate that an interface type declaration is intended to be a functional interface as defined by the Java Language Specification.

and the use case

Note that instances of functional interfaces can be created with lambda expressions, method references, or constructor references.

whose wording does not preclude other use cases in general. Since the primary purpose is to indicate a functional interface, your actual question boils down to “Are there other use cases for functional interfaces other than lambda expressions and method/constructor references?”

Since functional interface is a Java language construct defined by the Java Language Specification, only that specification can answer that question:

JLS §9.8. Functional Interfaces:

…

In addition to the usual process of creating an interface instance by declaring and instantiating a class (§15.9), instances of functional interfaces can be created with method reference expressions and lambda expressions (§15.13, §15.27).

So the Java Language Specification doesn’t say otherwise, the only use case mentioned in that section is that of creating interface instances with method reference expressions and lambda expressions. (This includes constructor references as they are noted as one form of method reference expression in the specification).

So in one sentence, no, there is no other use case for it in Java 8.