By now, we see there are 4 storage services on Microsoft Azure:
Azure Blobs: A massively scalable object store for text and binary data.
Azure Files: Managed file shares for cloud or on-premises deployments.
Azure Queues: A messaging store for reliable messaging between application components.
Azure Tables: A NoSQL store for schemaless storage of structured data.
If you don’t know how to use them well, Microsoft has alreay provided nice information which is "Deciding when to use Azure Blobs, Azure Files, or Azure Disks".
When to use Azure Files?
You want to “lift and shift” an application to the cloud which already uses the native file system APIs to share data between it and other applications running in Azure. OR, You want to store development and debugging tools that need to be accessed from many virtual machines.
When to use Azure Blobs?
You want your application to support streaming and random access scenarios. OR, You want to be able to access application data from anywhere.
When to use Azure Disks?
You want to lift and shift applications that use native file system APIs to read and write data to persistent disks.
You want to store data that is not required to be accessed from outside the virtual machine to which the disk is attached.