Yes apps is a remote mail server based on Gmail application. You can have email with your domain name and still host your webpages elsewhere. it is free for up to 10 users. I use it for all my clients and it works great. The only downside is lack of outlook support , which some of my client like.
With Google Apps, you can host your own mail, calendar and documents. You can learn more at http://google.com/a
Google App Engine lets you run 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 from your own domain name (such as http://www.example.com/) using Google Apps. Or, you can serve your app using a free name on the appspot.com domain. You can share your application with the world, or limit access to members of your organization.