Q: On aor later Hyper-V host, sometimes I see Host logical processors in the Processor area of Task Manager Performance--what is it and when is it visible?
A: Hyper-V is a Type 1 hypervisor, which means the hypervisor sits directly on the physical hardware. The virtual machines (VMs) or partitions communicate via the hypervisor, which includes the host or parent partition that manages Hyper-V--the OS you physically installed on the host.
Hyper-V allows each VM to use up to 64 vCPUs. This limit also applies to the management partition, because it too is accessing processor and memory via the hypervisor (this is often referred to as minimal root). However, generally there's no reason why the management partition would ever need more processors than this, since it should just be doing basic management and enabling access to certain types of resource.
To avoid confusion, if an administrator was looking at Task Manager on a Hyper-V host with more than 64 logical processors, Windows Server 2012 and later will show a Host logical processors value, which shows the number available to the host. That number will be different from the Logical processors value, which is the total number of logical processors in the host.
Note in the example on the left of the screen shot below that there is no Host logical processors value shown, because the host has only 64 logical processors. The right side of the screen shot shows part of Task Manager from a host with 128 logical processors, where the Host logical processors value is shown.