A hypervisor is the program that makes virtual machines possible. It sits between the physical hardware and the guest operating systems, deciding which guest gets the processor at any moment, partitioning memory, and mediating access to disks and network cards. To each guest it presents the illusion of a complete, private machine, while in reality it is multiplexing one set of hardware among many.
The older and more precise name for this component is the virtual machine monitor, or VMM. Popek and Goldberg’s 1974 paper laid out three properties such a monitor must provide: equivalence, meaning a program runs the same as it would on bare hardware; resource control, meaning the monitor stays in full charge of the physical resources; and efficiency, meaning the great majority of instructions execute directly on the real processor without monitor intervention. Their analysis showed exactly which processor designs could support a monitor meeting all three.
The Xen Project describes its own hypervisor as an open-source, type-1 (bare-metal) hypervisor that “makes it possible to run many instances of an operating system or indeed different operating systems in parallel on a single machine.” That single sentence captures why hypervisors matter commercially: by packing many isolated operating systems onto one physical server, they drive up hardware utilization and make it economical to rent computing in small slices.
Because the hypervisor controls the boundary between guests, it is also a security boundary. A well-built hypervisor keeps the failure or compromise of one virtual machine from spreading to its neighbors, which is what allows a public cloud to place competing customers on the same physical host.