Created a web role project on Azure. Looking at the service definition file I see that it adds a LocalResources section -
<LocalResources>
<LocalStorage name="ProjName.svclog" sizeInMB="1000" cleanOnRoleRecycle="false" />
</LocalResources>
It seems to be using this for writing the log files. Each Azure compute instance also comes with some memory. I am assuming that this LocalStorage would use the memory we get with that instance and not create a storage account. Is that assumption correct?
Local storage is temporary hard disk space available for each instance. It's configured as part of the virtual machine where your instance is hosted.
This is unrelated to table storage, blob storage or SQL Azure, and comes as part of the Web role or worker role. However, it's temporary, and will go away when your instance is recycled or rebooted.
There's a great article on what it is, how it works and how to use it from code here: http://vkreynin.wordpress.com/2010/01/10/learning-azure-local-storage-with-me/.