Google Sites lets non-techies create (primarily) static web sites. Google App Engine lets programmers create dynamic sites with persistent data and server code written in the Python language. In both cases, Google stores the applications on their servers and handles scalability for you! So if your great idea for a web application hits it big on Digg, slashdot or TechCrunch, your application will be able to handle the load (with a little help from your friends Larry Paige and Sergy Brin).
Google App Engine is a manifestation of cloud computing:
where IT-related capabilities are provided “as a service”, allowing users to access technology-enabled services "in the cloud". It is a general concept that incorporates software as a service, Web 2.0 and other recent, well-known technology trends, where the common theme is reliance on the Internet for satisfying the computing needs of the users without knowledge of, expertise with, or control over the technology infrastructure that supports them.
Getting Started with App Engine at USF