A hypervisor is system that manages virtual machines, such as VirtualBox, QEMU, or Xen. Some hypervisors, such as Xen, run on bare metal and do not require a host OS (although they may require a hosted OS to serve as a control interface). Others, such as VirtualBox and QEMU, run inside a host OS. Some, such as QEMU, allow for simulating different machine architectures; others, such as VirtualBox, do not (i.e., the VM architecture is always the same as the real host). Simulating an architecture requires more resources, just as real VMs require more resources than containers.
Hypervisor style virtualization is called platform level virtualization.