How do I clear the content of a div using JavaScript?

You can do it the DOM way as well:

var div = document.getElementById('cart_item');
while(div.firstChild){
    div.removeChild(div.firstChild);
}

Just Javascript (as requested)

Add this function somewhere on your page (preferably in the <head>)

function clearBox(elementID)
{
    document.getElementById(elementID).innerHTML = "";
}

Then add the button on click event:

<button onclick="clearBox('cart_item')" />

In JQuery (for reference)

If you prefer JQuery you could do:

$("#cart_item").html("");

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