I think that you should specify your question a little bit. What do you exactly want to know? Azure is a big platform with a wide range of usage scenarios.
In general Windows Azure is Microsoft Cloud Computing platform and you can do a lot with it. On the one hand it can be used as a development platform and on the other hand as a virtualization platform (and of course a lot of things).
To become a little bit familiar with Azure you should visit the following sites:
Windows Azure provides many services. Each services has its own usage.Broadly speaking, the services that Windows Azure provide can be separated into two categories, a) IaaS, infrastructure as a service, b) PaaS, platform as a service.
IaaS is basically providing data center hosted virtual machine. Many organizations prefer to use Microsoft Windows Azure hosted VM instead of managing those themselves to simplify the logistics and reduce costs.
PaaS is cloud computing platform technology, for example Blob Storage, Table Storage, Queue, SQL Azure, Service Bus, Media Services, and Mobile services. Each services has its own set of use cases, for example, Blob storage enables Windows Azure application
to read/write/update/delete large binary objects in data center.