Yes it is possible to have static class definitions inside an interface, but maybe the most useful aspect of this feature is when using enum types (which are special kind of static classes). and one case where I've found it useful is when an interface has to throw custom exceptions. You the keep the exceptions with their associated interface, which I think is often neater than littering your source tree with heaps of trivial exception files.
interface MyInterface {
public static class MyInterfaceException extends Exception {
}
void doSomething() throws MyInterfaceException;
}