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This has a nice name – a lazy function definition. A lazy function is one that pretends to work but it doesn't really.

It does some work initially and then caches the result. Then on consecutive calls it only returns the pre-computed result, it doesn’t really do anything.

In order to do so, the function redefines itself with a new implementation, one that simply points to the computed result.

function lazy() {
    var result = 2 + 2;
    lazy = function() {
        return result;
    };
    return lazy();
}

lazy(); // 4
lazy(); // 4

Next pattern – a function that overwrites itself, a self-redefining function. Pretty similar to functions that return functions, but this time the function is re-implemented from the inside, not returned.

function next() {
    var count = 1;
    next = function() {
        return ++count;
    };
    return count;
}

next(); // 1
next(); // 2

Functions are objects, so they can be passed around like callbacks for example and also returned by other functions.

You call a function that does some complicated setup and as a results returns a new function. You assign the result to a new function and use it afterwards.

function setup() {
    alert(1);
    return function() {
        alert(2);
    };
}
var my = setup(); // alerts 1
my(); // alerts 2

Your setup function can store some private data in a closure and use that data somehow.

Here setup() creates a counter function, which gives a next ID for example. But the count variable is not exposed.

function setup() {
    var count = 0;
    return function() {
        return ++count;
    };
}
var next = setup();
next(); // 1
next(); // 2

Functions are objects, it’s very important to keep that in mind.

Functions are objects so they can have properties. And they they have methods.

They can be copied, deleted, passed as arguments to other functions, returned by other functions.

They also provide scope.

And they have special feature that sets them apart from the other objects – they are invokable, they can be called.