Customers using Azure generally create VMs in the Cloud to connect to databases that also reside there. But, for many reasons, some companies would rather keep their data on-premises and not host it in someone else's datacenter.
For those companies with this need, Microsoft provides a special Hybrid Connection client that allows connections back to the local datacenter so that data can be made available to Azure VMs.
You install the client onto the VM in Azure (or can be installed in the web/worker role instance), and then use the supplied PowerShell cmdlets to configure the connection.
The download is here: Microsoft Azure Hybrid Connection Client