Hyper-V in Windows Server 2012 saw improvements to Dynamic Memory that included support for configuring minimum memory.
While Windows 2008 R2 SP1 did allow you to configure ‘minimum memory’ (called Startup RAM), Windows VMs use a larger amount of memory just for startup. As such, admins would set the minimum memory to more than it needed to be, just for the purposes of having sufficient memory at startup. While this worked, the downside is that unused memory was left stranded on each VM.
So in Windows Server 2012, a setting was added specifically for minimum memory. So now you set the amount of memory used just during the startup time and have a minimum setting that is lower, allowing the host to lower the memory assigned to the VM if needed.
NOTE: My screenshot shows the startup and minimum settings at the same amount. Normally the startup setting would be higher.