What Codename One is...
The foundation that allows you to do Write-Once-Run-Anywhere on mobile. This includes all of the tools required to convert JVM bytecode into native executables on each mobile platform. You dont need to worry about these, since this is all handled seamlessly by the build server.
A simulator that allows you to test and debug your app right inside your IDE.
What Codename One is NOT...
Want to use some HTML in your app? No problem! Codename One has a WebView widget that will allow you to wrap HTML5 inside your app seamlessly.
Unlike some other toolkits that merely provide bindings to native components and APIs, Codename One's UI component library is light-weight and truly cross-platform. This provides 100% code reuse across platforms, not only for business logic, but for the UI also.
Yes you can! In fact you can even mix native widgets and light-weight widgets together inside a Codename One app seamlessly.
Yes, you can access both system APIs and 3rd party native frameworks and libraries.