Hypervisor: The hypervisor is to Hyper-V what the kernel is to Windows. The hypervisor is not all of Hyper-V, it is just the lowest level component that is responsible for interaction with core hardware. The hypervisor is responsible for creating, managing and destroying partitions. It directly controls access to processor resource and enforces an externally delivered policy on memory and device access. To give some perspective: the hypervisor is just over 100k in size, the entire Hyper-V role is around 100mb in size and a full installation of Windows Server 2008 with Hyper-V will be multiple gigabytes in size. Once you have installed the Hyper-V role the hypervisor is loaded as a boot critical device.
Virtualization Stack: The virtualization stack is everything else that makes up Hyper-V. This is the user interface, management services, virtual machine processes, emulated devices, etc...
Partition: A partition is the basic entity that is managed by the hypervisor. It is an abstract container that consists of isolated processor and memory resources - with policies on device access. A partition is a lighter weight concept than a virtual machine - and could be used outside of the context of virtual machines to provide a highly isolated execution environment.
Root Partition: This is the first partition on the computer. Specifically this is the partition that is responsible for initially starting the hypervisor. It is also the only partition that has direct access to memory and devices.
Parent Partition: The parent partition is a partition that is capable of calling the hypervisor and requesting that new partitions be created. In the first release of Hyper-V the parent and root partitions are one and the same - and there can only be one parent partition.
Microsoft, WS2008, Windows Server 2008, Win2K8, Hyper-V, Terminology