vSphere is the VMware software stack that implements private-cloud data center management and the on-premises component of hybrid-cloud deployments.

A vSphere installation includes one or more instances of vCenter Server configured to manage one or more virtual data centers. Each virtual data center includes one or more instances of VMware ESXi.

The vCenter Server Appliance contains an instance of vCenter Server. The appliance Management API gives you programmatic access to manage the management elements of your data center.