The best thing in BLOB store is variety of use types. You can keep your VHD files, backups, application files, source code and packeages and whatever you need. You can even put data files for your SQL Server databases and attach these to SQL Server running at Azure Virtual Machine, and it will give you significant increase of speed. Security options are great, you can grant and revoke access using powershell, you can even create tokens for temporary access, so you will not need to revoke access, when token expires. Virtual Network integration was added recently, so your storage can be accessed within VNET, without need to send traffic outside of your resource group. Different replication options can provide data resiliency on desired level without unneeded spend of funds. Different access methods could be useful in different cases. You can access your storage using PowerShell, Azure Portal, Storage Explorer tool by Microsoft and even SQL Server Management Studio. The last one is very useful when you are using BLOB storage paired with SQL Server, so you can manage both from single window.
Paid outgoing traffic from Azure, you can put anything to BLOB storage for free, but you will be charged for getting it back.