Microsoft’s Mark Russinovich published a blog post that goes into detail about how the newly released Azure File Service takes advantage of existing Azure services to provide a hyper scale file share service. The key is the implementation of SMB 3.0 support with directory and file metadata being stored in Azure Table Storage while the files themselves are stored in Azure Page Blob.
A benefit of using these internal Azure technologies to implement Azure File Storage is that we are able to provide a REST interface to Azure file shares. Applications can use the REST interface for a file at the same time that clients invoke the SMB interface because the REST API honors SMB Leases, byte range locks, change notifications, and more, just as SMB clients do. — Azure Blog
The support for SMB 3.0 also enables support for encryption and persistent handles. The diagram below shows how files are accessed from both On-Premise clients and Azure clients.
For more information on how Azure File Storage works, read Mark Russinovich’s blog post on the Azure Blog.