Because setting the div's display style property to "" doesn't change anything in the CSS rule itself. That basically just creates an "empty," inline CSS rule, which has no effect beyond clearing the same property on that element.
You need to set it to something that has a value:
document.getElementById('mybox').style.display = "block";
What you're doing would work if you were replacing an inline style on the div, like this:
<div id="myBox" style="display: none;"></div>
document.getElementById('mybox').style.display = "";