Microsoft has published a really good white paper on Azure Data Security. You can find the paper here.
The paper focuses on key issues around allocation of customer storage space and how this storage is secured during allocation and when it is de-allocated. Microsoft outlines how customer data is destroyed as it is de-allocated so that there is no method for another customer getting access to that data if they are randomly allocated a previously used storage block.
In a shared storage service such as Azure, this protection of customer data is a fundamental requirement for ensuring that your data is protected from other customers (and/or malicious hackers).