<p>Today's date is: Friday, August 15, 2014</p>
Unfortunately, you'd have to change the date by hand if you wanted to keep it up to date every day!
But with PHP, you could do it this way (with your page ending in .php and not .html):
<p>Today's date is: <?php echo date("F j, Y"); ?></p>
Then PHP will keep updating the date automatically each time the page is accessed.
PHP is also good for grabbing the contents of a database, writing it as HTML, then displaying it on the screen.
One difference between PHP and HTML: if the page is all in HTML/CSS, then the page goes straight from the server to the browser as is, because HTML is the browser's natural language. But if it is in PHP, the page goes to the server first to run the PHP script (such as the date code above is changed into a real date in HTML code), changed to HTML, then sent to the browser.
I hope this helps you a little bit. If you haven't done any programming yourself, then you can expect a long period of time learning before getting a website up and running. But if you use the services of the company you linked to, you can get the site up quickly and spend your time learning to use that site.