If u want a quick introducion on how Google Apps Engine works, take a look at the below two videos and read this blogpost.
Google App Engine lets you run your web applications on Google’s infrastructure. App Engine applications are easy to build, easy to maintain, and easy to scale as your traffic and data storage needs grow. With App Engine, there are no servers to maintain: You just upload your application, and it’s ready to serve your users.
You can serve your app using a free domain name on the appspot.com domain, or use Google Apps to serve it from your own domain. You can share your application with the world, or limit access to members of your organization.
App Engine costs nothing to get started. Sign up for a free account, and you can develop and publish your application for the world to see, at no charge and with no obligation. A free account can use up to 500MB of persistent storage and enough CPU and bandwidth for about 5 million page views a month.
During the preview release of Google App Engine, only free accounts are available. In the near future, you will be able to purchase additional computing resources.
Google App Engine has enough documentation. So if u are interested to create an app, check out the documentation here
BTW the service is available only for the first 10,000 developers who applied @ http://code.google.com/appengine, and Im one among them 😉 I got an invitation yesterday.