Why use the callback function in this case?

I'm guessing you're refering to this code at about 0:30 in the video:

$('button').click(function() {
    console.log('Done!');
});

Since click() sets up something to handle an event that will happen at an indeterminate time in the future it requires a function that it will call when that event occurs. That is essentially what a callback function is.

You can pass the console.log function directly to click of course, so whenever the button in clicked it will call console.log() as it's callback:

$('button').click(console.log);

The trouble is, what are we passing to console.log? When we pass console.log directly we aren't able to pass along arguments. We won't be passing along the simple string "Done!" Instead it will be passed what every event handler is passed, the event object, and it will log that to the console instead.