I recently installed VirtualBox on our Hetzner Dedicated Server (Running Windows Server 2012) to host a Ubuntu Server VM.
After selecting the dynamically resize option, I presumed that the size of the VM would increase as space is requited. It seems that this is not the case.
You select the MAX size of the VM, then the vdmi file only takes up the space it uses, up to a maximum of the MAX size that you specified.
Looks like the folks from VirtualBox didn’t make it easy to change the size of the VM. This has to be done in the Windows command line run as Administrator. Also, after resizing the VM running linux, you have to boot from a Live CD, and change the partition size.
See this post for resizing a VirtualBox VM: