Windows Azure is Microsoft's answer to the well known Cloud Computing.
Windows Azure tries to answer the following problems:
One of the problems faced during deploying applications is the future scalability. The current hardware capacity seems to be limited and we need to either upgrade the server or add new servers with a load balancer. These overheads are threatening the scalability of the application.
Windows Azure targets to address this problem. It provides an easier solution to Scalability.
To cater the increasing demand, more hardware has to be purchased, install operating a system, install the application and support it. This tremendously increases the cost of the application.
Windows Azure targets to address this problem. It reduces cost involved to cater increasing demand.
In the current software development world, the developer and the support team needs to think about the application logic + support strategies (like performance, load balancer installation and maintenance). Thus there are more things to worry about other than the core business logic and features.
Windows Azure targets to address this problem. It allows the developer to concentrate just on application features.
The quote of Microsoft on Azure says that "Focus on your Application. Not the infrastructure."