W3C school provides its tutorial.
history: HTML->mobile->HTML5->jquery mobile
JQM is a touch-optimized web framework for creating mobile web apps.
JQM uses HTML5 & CSS3 for laying out pages with minimal scripting, trying to make a page look like a mobile native app page.
JQM tries to use styling, making the pages look like mobile native apps.
jQM is built on top of the jQuery library.
jQM works in desktop also, it has mobile flavor. You can simulate the test in mobile devices by sizing the screens.
One html file for jQM has serveral pages.
Framework, like jqm is file-base, not site-based.

When you use any web client, you can have make a regular page request, or you can accessing a REST service. The later case, the REST service is a partition, which also can be use by other web clients and native mobile apps.
Naturally, any native mobile apps must use REST services.
Unlike web, the native apps uses REPT, read-eval-print loop. Native mobile apps use their compilers. It detects some error during development time.
If you can use web, instead of native mobile app, do it. If you are already comfortable with native mobile apps, just do so. Native mobile apps have more involvements.

jQuery Mobile Topics