I can answer your question partially..
"Azure" is project name from Microsoft for Cloud Computing.
Benefit for Asp.Net Developer:
Cloud Computing will give you hardware independence.
You don't have to worry about traffic to your Web Apps, means if traffic to web Applcation increase or decrease dramatically, your application works fine .
Demerit for Asp.Net Developer:
your Application should be completly stateless, as you said you have existingwebsite in Asp.Net , then may be you are using Session variable to maintain state ... but in cloud computing you will not have session variables .
So you have to change your existing application alot to make compatible with cloud computing.
Following are few links for startup, I hope it will help you
http://www.msdev.com/Directory/SeriesDescription.aspx?CourseId=96Arjunpktr, if this helps please login to Mark As Answer. | Alert Moderator