Steve Marx, a Microsoftie who works on Windows Azure, has created a video with narration called What is Windows Azure. Completely drawn by Steve, he starts with a very simple introduction to cloud computing and why we need it and then on to Windows Azure and its components. This video even helped me to get a better understanding of how cloud services work and how we can benefit from them.
Video: What is Windows Azure?
P.S. You might want to check out the pricing structure of Windows Azure as well.
I used to have Windows Azure on my laptop nut I have upgraded it to WIndows 7. Is there a a new Windows Azure or the latest version?