Disclaimer: I'm the CometD project leader.
CometD is a set of library to write web applications that perform messaging over the web.
Whenever you need to write applications where clients need to react to server-side events, then CometD is a very good choice. Think chat applications, online games, monitoring consoles, collaboration tools, stock trading, etc.
See more at the preface.
CometD ships a JavaScript client library, a Java client library and a Java server library.
This allows you to write applications in the browser with fine-grained logic and control on the server.
The server library, being in Java, leverages the high scalability of the JVM and the powerful asynchronous I/O API that the JVM and the Servlet specification provide.
CometD is transport agnostic: you write your applications using high level APIs, and CometD takes care of delivering the messages over the wire using the best transport available: WebSocket or HTTP, also providing a transparent fallback in case WebSocket does not work.
CometD provides a clustering solution called Oort that allows you to scale horizontally your web applications.
CometD comes with a ton of features and an extended documentation along with tutorials and demos you can use as a starting point for your project.
Join CometD to start hacking on your CometD-based web applications.
The CometD tutorials are currently written for CometD 2.x, but a port to CometD 3.x (the current version of CometD) is currently underway, so that requires a bit of patience.
But you can start right away by following the primer and deploying the demos.
I hope you can get started with CometD with the above references.
Drop an email on the mailing lists for any help you may need.