Hyper-V is Microsofts proprietary hypervisor. Since Server 2012 / 2012 R2 it can be installed as role in a full Windows OS, the stripped down Windows OS Server-Core mode or the standalone Hyper-V Server.
The Hypervisor itself is only <1MB in size as Hyper-V uses a driver model similar to e.g. Xen, which provides device drivers not with the hypervisor kernel but as part of a parent partition/domain0 operating system instance. Hyper-V uses paravirtualization and hardware-assisted virtualization.
The disk footprint varies from about 5GB for Hyper Server and Server Core to 10GB+ for the full install (please note that these are not the installation recommendations, e.g. for Hyper-V Server 2012 (as with 2008 R2) on USB Microsoft recommends a min of 8GB)

In Windows Server 2016, Microsoft brings the Nano Server which enables to install Hyper-V on a low footprint OS (almost 1GB on disk). Nano Server requires the Software Assurance