Icenium is environment for creating hybrid apps that run on mobile devices and as such, offline mode should be taken into account. Using a designated DB server would always require your app (respectively the user's device) to have connectivity available. With that said, a good starting point on storing data in HTML application is this page
. Icenium supports the SQLite Cordova plugin. You can use it to create, update and query a native sqlite database that is stored on the device's filesystem and is permanent until you delete it or the user uninstalls your app.
If you MUST use a designated DB server, you can check this nice introduction to WebAPI, REST, JSON, AJAX with SQL as datasource here