The hypervisor is a thin operating system that sits between the hardware and the virtual machines.
XenDesktop is virtualization software, but it has to run on something. That something is hypervisor software.
Note
Tribal Knowledge says that you can run XenDesktop on physical hardware without any hypervisor; however, there aren't many use cases for this.
For reference, in a Type-1 hypervisor deployment, XenDesktop runs on top of an operating system, which runs on top of a hypervisor, which runs on top of the server physical hardware.
The supported hypervisor operating systems are as follows:
Citrix XenServer 6.0.2, 6.1, 6.2, and 6.5
VMware ESXi 5.0 update 2, vSphere 5.1 update 1, and vSphere 5.5 update 2
Microsoft Hyper-V 2012 R2, 2012 SP1, or 2012
Note
To see a list of server hardware that is compatible with the hypervisor you choose, search for a hardware compatibility list for hypervisor on the Internet, or go to the following links:
XenServer HCL: http://bit.ly/hcl-xen