A hypervisor, in most contexts, is the software that creates and runs virtual machines. VMWare is an example of a hypervisor that you might use for running a different OS on a personal work computer (eg. running Ubuntu on a computer whose main OS is Windows 11). AWS has its own Nitro hypervisor that is being used to create EC2 instances.
In kernels, the position of highest privilege is called the supervisor. The prefix ‘hyper-’ is a stronger variant of the prefix ‘super-’, so the hypervisor is named such because it is basically the supervisor of supervisors.
The computer that runs a hypervisor is called a host machine while the virtual machines within are call guest machines. Hypervisors handle resource allocation to guests VMs, eg. it handles CPU scheduling among other things.