A hypervisor is sort of like a replacement OS and virtualisation layer in one.
You install the hypervisor first, then allocate additional virtual machines for each OS you install. The hypervisor itself is extremely light weight and only concerned with managing the virtual machines, as a result you can get very close to "bare metal" performance from your VMs. The hypervisor management applications all run in a VM themselves (with special permissions) to keep the virtualisation layer as thin as possible.
Depending on the features of your chosen hypervisor you can even have one VM thinking it was on an Intel machine and another thinking it's on AMD, both on the same physical hardware. Aside from folks doing development work I don't see much application for that, but it's possible. Putting extra translation overhead between the VM and hardware also slows things down.