Simply put, Azure is a multi-regional cloud computing platform from Microsoft. Split across 30+ worldwide datacenters, the Azure platform provides a highly redundant cloud platform in which you can run your applications, infrastructure, etc.
With a "pay-as-you-go" pricing model, Microsoft assures that you only pay for what you need. As such, you are able to scale up and down on an "as-needed" basis and only pay for the resources you use.
Because Azure supports a broad selection of operating systems, programming languages, frameworks, tools, databases and devices, it allows you to extend virtually any existing IT environment into the cloud. Common uses for Microsoft Azure include everything from hosting your corporate website to extending your on-premises Active Directory to the cloud for redundancy.
To learn more about Microsoft Azure, click here.