jsfiddle has wrapped it automatically in the onload event. You haven't done this in your HTML page, so when it runs in the browser you're trying to get hold of the div before it's been rendered, so theDiv is null.
The below should work:
<!doctype html>
<html>
<head>
<script src="http://code.jquery.com/jquery-latest.min.js" type="text/javascript"> </script>
</head>
<script type="text/javascript">
window.onload = function () {
var random = 0;
var theDiv = document.getElementById("showVal");
updateTheDiv(9, 0);
function updateTheDiv(inRange, inMin) {
random = (Math.random() * inRange + inMin) | 0;
theDiv.innerHTML = random;
var nextCall = (Math.random() * 1000) | 0;
setTimeout(function () {
updateTheDiv(inRange, inMin);
}, nextCall);
}
}
</script>
<body>
<div id="showVal">
</div>
</body>
</html>
