There are several solutions to your problem, I will enumerate them from the easiest ones to harder solutions.
If you have an easy app you can test it in jsFiddle web tool. It can provide almost full jQuery Mobile functionality except form submitting and multi HTML support.
Here's a easy jQuery Mobile jsFiddle example: http://jsfiddle.net/Gajotres/yWTG2/
When you want to test it just go to the Share option and click full screen like this:
http://jsfiddle.net/Gajotres/yWTG2/embedded/result/
A good thing about jsFiddle is that you don't need to have a full HTML (like in my example), you can test it just with basic page HTML:
<div data-role="page" id="index">
<div data-theme="a" data-role="header">
<h3>
First Page
</h3>
<a href="#second" class="ui-btn-right">Next</a>
</div>
<div data-role="content">
</div>
<div data-theme="a" data-role="footer" data-position="fixed">
</div>
</div>
Example: http://jsfiddle.net/Gajotres/fEV3J/
Hosting
If you have you own web hosting just upload your files and test it over the internet.
Local Web server
You can install a PHP web server package on your local computer and test everything in your local LAN. PHP is not needed for this, we only need an configured Apache server. While you can download it separately and install it by your self it is much easier to download prebuild package like:
Phonegap is a mobile app framework that servers as a wrapper between a native app and a web app. You can use it to create a hybrid mobile application, basically a web application that acts as a native mobile application.
I am not going to write any more about this solution because there are numerous other answers about this topic, but to make it easier for you here's my other answer regarding Phonegap and jQuery Mobile: https://stackoverflow.com/a/14166593/1848600