ESX Server is VMware's flagship virtualization product being first released in 2001 and quickly becoming the market leader in the server virtualization space. The core ESX component is part of the wider Virtual Infrastructure offering, providing enteprise management capabilities and enhanced reliability functionality.
ESX itself is based on Linux and consists of a kernel and support files, which are installed during the installation process and stored onto persistent storage such as an array of disks. This provides the hypervisor capability which allows for the hosting of multiple virtual machines on the physical host.
Virtual Infrastructure 3.0 (VI3) is the name given collectively to the components which provide virtualization including ESX and management components including vCenter. VI3 has been named to VMware vSphere in it's 4th generation incarnation and includes updated components including ESX 4.0.
There is also an ESXi variant which is a stripped down version of the standard ESX version, providing a smaller footprint of just 32MB for installation. This is accomplished by removing some of the additional features which allow for a simpler management configuration. ESXi is itself also available in two variants, ESXi Installable and ESXi Embedded, with the latter being available on board a memory chip.
vCenter serves as a centralised management tool for ESX/ESXi and the virtual machines they host. It is sold as an optional extra but for enterprise environments it is considered essential as it provides:
• ESX/ESXi hosts and virtual machines management (including resource management)
• Template Management
• Virtual Machine deployment and management
• Statistics and Logging
• Alarms, Event Management and Task Scheduling
More importantly the enterprise features such as vMotion (moving live virtual machines), HA (restarting crashed virtual machines automatically) to DRS (dynamically allocating resources) won't work without vCenter.