Well Windows Azure is an open, flexible cloud platform which enabled you to quickly build, deploy and manage multiple application across a global network of data centers managed by Microsoft
It’s always up, always online and ready for your use. For the most part its features are limitless and allows the user (or company) to grow out as much as he/she (them) need.
To simplify: You get access to computer/server resources that you don’t need to own, buy, power up or provide resources such as CPU, Memory, Storage or networking. It’s just there, waiting and ready for you.
More info on the Azure Website: http://www.windowsazure.com/en-us/