What is the (function() { } )() construct in JavaScript?

It’s an Immediately-Invoked Function Expression, or IIFE for short. It executes immediately after it’s created.

It has nothing to do with any event-handler for any events (such as document.onload).
The first pair of parentheses (function(){...}) turns the code within (in this case, a function) into an expression, and the second pair of parentheses (function(){...})() calls the function that results from that evaluated expression.

This pattern is often used when trying to avoid polluting the global namespace, because all the variables used inside the IIFE (like in any other normal function) are not visible outside its scope.
This is why, maybe, you confused this construction with an event-handler for window.onload, because it’s often used as this:

(function(){
    // all your code here
    var foo = function() {};
    window.onload = foo;
    // ...
})();
// foo is unreachable here (it’s undefined)

Correction suggested by Guffa:

    The function is executed right after it's created, not after it is parsed. The entire script block is parsed before any code in it is executed. Also, parsing code doesn't automatically mean that it's executed, if for example the IIFE is inside a function then it won't be executed until the function is called.