Computer virtualization allows resources from one powerful server to be split among many smaller servers. This lets you manage resources more effectively, e.g. moving memory and CPU resources between virtual machines, turning machines on and off as needed, and moving machines to new hardware with minimal downtime. VMware describes vSphere as their virtualization platform – i.e. an operating system and set of administrative tools.
Hypervisor is a term used to refer to the system drivers that manage splitting resources between virtualized machines. This allows many guest machines to run on a single host. Hypervisors either run directly on machine hardware (a “bare-metal” hypervisor) or as a process within a host operating system. VMWare ESX/ESXi are the first type, and Oracle VirtualBox and Microsoft VirtualPC are of the second. Competing products include Xen and Microsoft Hyper-V.