What does "return function() { ... }" do in JavaScript?

Question

Recently I saw this piece of JavaScript code, but have been unable to understand what it is trying to do.

var f = function(a) {
    return function() {
        alert(a());
    };
};
f(function() { return "Hello World"; })(); 

Please explain what this accomplishes!

Answer 1

It executes the function that f returns.
f returns a function that calls an alert that displays the output of the function you gave as parameter to f.

EDIT: Just substitute some parts to make it easier on the eye and you will see yourself:

var f = function(a) {
    var output = a();
    var alertCaller = function() {
        alert(output);
    };
    return alertCaller;
};

var helloWorld = function() { return "Hello World"; }
var result = f(helloWorld); //f takes a function as argument
result(); //result must be a function