jQuery Mobile by itself can't do this. It can help with the user interface part of your app.
You will need to use something like Phonegap, Titanium, Rhodes, etc. that uses an embedded browser control to create a native app. Then you can use jQuery Mobile to handle aspects of the UI.
Alternately, you could create a "webapp", which is not a true native app. Again, jQuery Mobile can be useful as part of the solution, but you will need to create code to access a local database use HTML5 local storage. jQuery Mobile doesn't provide any support for this, you will need to write your own code or choose some library that supports local storage.