function() { alert( "You pressed the mouse button" ); }

One use of anonymous functions is to pass them as arguments to other functions.

If a function doesn’t have a name, and it’s just another value in the machine, then functions in Javascript are much closer to data than what we would consider traditional functions and objects. It’s data that does stuff to be sure, but in every place that matters, learning to look at the function as a piece of active data will really help you out when it comes to figuring out just how to apply this technology. hunlock.com

First lets look at a function that abstracts iterating over an array so that we can use an anonymous function to actually do something interesting.
Looping over an array and applying an action to it is easy. Take the following code:

function forEach(array, action) {
  for (var i = 0; i < array.length; i++)
    action(array[i]);
}

forEach (["Neil", "Jen", "Nelson"], console.log);
forEach (["Neil", "Jen", "Nelson"], alert);

The first sends each item of the array to the console and the second to the alert() function.

Now lets define a function called map will use the iterator function forEach() that we’ve defined above and call it.

function map(func, array) {
  var result = [];
  forEach(array, function (element) {
    result.push(func(element));
  });
  return result;
}

map( Math.round, [0.01, 2, 9.89, Math.PI] );

#outputs - [0, 2, 10, 3]

So the first argument is a function that rounds each one of the following array items.