There are two possible approaches that you could take:
One option is to develop your own backend server that offers push, pull, and notification services. This server would communicate with your database and provide JavaScript-accessible services (likely utilizing Ajax. Keep in mind that Ajax is a concept, and you'll need to choose an implementation, such as the one offered by jQuery/jqMobile frameworks). For a quick and easy setup, you might consider using a platform provider like dotCloud.com, which offers preconfigured servers and keeps you within the same programming language/environment (e.g., utilizing Node.js and dotCloud's MySQL service).
Alternatively, you could opt for a pre-built backend data server like parse.com or deployd.com. These options come with a complete framework and necessary interfaces for remote data storage and real-time updates for clients. Additionally, they ensure scalability for your application.
The first approach is more suitable if you're interested in learning how to program a backend server, but it comes with the responsibility of ensuring security and scalability.
On the other hand, the second approach is ideal if you prefer to focus on getting your app up and running without delving into the minutiae of building and managing a backend server.
Disclaimer: I have no affiliation with any of the platforms or products mentioned, and I'm simply using them as examples. There may be other similar offerings that are more suitable or have less commercial affiliation.
EDIT: Fixed typos and domain names