Web browser V Add to Home Screen V Native Shell

The three main ways to present an HTML5 app on a smart phone or tablet are:

Web Browser

This is the simplest option: you access your web application through the web browser. You can also develop your web application to work (or at least partially work) when offline.

The good news is that you don't need to write any native code or join any developer programme.
The downsides are that it does not look like an "app", and there is no access to some of the hardware e.g. camera.

Add to Home Screen

This is one step above using a web browser.

You get a more "app-like" experience, but there is still no integration with the smart phone or tablet hardware.

Native Shell

In this option, you write a small amount of native code for each smart phone platform - iPhone, Android or Windows.
The native code runs a web browser, which runs your HTML5 application.

The upside is that you can access all the hardware: GPS, camera, gyroscopes etc.
However, you will have to join the develper programmes and may need to share your in-app income with the app store.

Apache Cordova is coming soon; an open-source version of PhoneGap. This will provide most of the native shell code for you.