Azure disks are stored as page blobs in Azure Storage. A storage account has specific scale targets. As you drive heavy disk I/O load through a VM, it's possible to push the limits of these storage targets. Locally-redundant storage accounts have a perf target of 10Gbps ingress/15Gbps egress, while geo-redundant accounts have a target of 5Gbps ingress/10Gbps egress. A specific blob (which holds a single disk) has a target of 60MBytes/sec.
This is why you will see suggestions (such as that TechNet video) for using multiple disks across multiple storage accounts, to go beyond account-specific storage scale targets.
Here's an article regarding VM sizes and related max IOPs. You'll see that each VM size has max. IOPs equivalent to 500 x #disks attached.
This article covers performance considerations for running SQL Server in a virtual machine, that covers many topics including disk IO.