This about is taken directly from the JQuery Mobile website:
http://jquerymobile.com/about/
"jQuery Mobile is a HTML5-based user interface system designed to make responsive web sites and apps that are accessible on all smartphone, tablet and desktop devices. It is built on the rock-solid jQuery and jQuery UI foundation, and offers Ajax navigation with page transitions, touch events, and various widgets. Its lightweight code is built with progressive enhancement, and has a flexible, easily themeable design." - JQuery Mobile team
I would strongly recommend going to the site to learn more about JQuery Mobile. This is just an excerpt to help beginners.
You can also find more examples and information on the jquery-mobile official page: https://jquerymobile.com/demos
The current version of JQuery Mobile is 1.4.5 and can be downloaded here: https://jquerymobile.com/
In the code below the javascript and css files are included by URL. You can alternatively follow the bullet points above and include it by the path it's located at on your local machine, i.e.:
<link href="lib/jqm/jquery.mobile-1.4.5.min.css" rel="stylesheet" />
...
<script type="text/javascript" src="lib/jqm/jquery.mobile-1.4.5.min.js"></script>
These are the minified versions of the css and js files. You can alternatively include the non minified version during development so that it's easier to read if you need to dig into it. If you do so I would recommend switching them back to the minified versions upon deployment to production.
<!-- it is imported inside head tags. -->
<!-- no additional files needed, if css and js referred with full path. -->
<!DOCTYPE html>
<html>
<head>
<!-- Viewport setup. -->
<meta name="viewport" content="width=device-width, initial-scale=1">
<!-- jQuery Mobile styles come first before js. -->
<link rel="stylesheet" href="http://code.jquery.com/mobile/1.4.5/jquery.mobile-1.4.5.min.css">
<!-- Basic jQuery library -->
<script src="http://code.jquery.com/jquery-1.11.3.min.js"></script>
<!-- jQuery Mobile library kind of extends upon jQuery -->
<script src="http://code.jquery.com/mobile/1.4.5/jquery.mobile-1.4.5.min.js"></script>
</head>
<body>
<!-- example page element using jQuery mobile tags: -->
<div data-role="page" id="pageone">
<div data-role="header" id="pageone-header">
<h3>Insert Page header Here</h3>
</div><!-- /header -->
<div role="main" class="ui-content" id="pageone-content">
<center><h3>Page title</h3></center>
<!-- All HTML for the page content goes here -->
</div><!-- /content -->
<div data-role="footer" data-position="fixed">
<h4>Insert Page footer Here</h4>
</div><!-- /footer -->
</div>
</body>
</html>