I do not believe the code you have presented has any faults in any way. I believe it is to do with your loading of the JQuery library, as with the following code I achieved these results:
index.html
<html>
<head>
<script src="jquery.js"></script>
<script>
$(document).ready(function() {
$('#main').click(
function(){
$('#news').load('news.html');
}
); //end click
}); //end ready
</script>
</head>
<body>
<p id="main">HELLO</p>
<p id="news">NEWS</p>
</body>
</html>
news.html
<html>
<head></head>
<body><h1>HELLO STACK OVERFLOW!!!</h1></body>
</html>
Before click:

After click:

However, when I was building this example I first tried using the Google APIs version of JQuery and found that I could not currently connect to the API. Therefore I believe the solution to your problem is to go to this website: http://code.jquery.com/jquery-1.11.1.js and copy and paste everything into a text file called 'jquery.js'. Then add the following to the head tag of your main HTML file:
<script src="jquery.js"></script>
Make sure that 'jquery.js' is in the same directory as the main HTML file of your project otherwise this will not work. Hope this helps :)