VMWare, from VMware, Inc., is a series of three software packages intended to provide virtual machine technology to Windows and Linux; VMWare Workstation, VMWare GSX Server, and VMWare ESX Server. It allows one to run one or more operating systems "on top" of the host operating system, each in their own virtual machine or VM. Each VM gets its own virtual computing resources such that the operating system inside of it is unaware that it is running inside a virtual machine.
What makes VMWare special compared to products such as Virtual PC or bochs is that rather than emulating the processor, it "virtualizes" instructions, simply passing instructions (or groups thereof) to the CPU for execution. This is both its strength and its weakness. VMWare provides very fast execution, but can only run on platforms using the x86 instruction set.
The ESX and GSX server products primarily differ from the Workstation product in that they provide an architecture which allows for connecting to the virtual consoles of VMs remotely, as well as providing integration through COM and Perl. This makes them far more useful for running servers than the Workstation product, which is primarily useful for testing applications, or for getting full application compatibility on a different operating system. For instance, if you need to run Linux on your system, but require Windows software which will not work with WINE, then you can run Windows in a VM and run your programs there. Alternatively, you can run an X Server on Windows, run Linux in a VM, and set your DISPLAY variable such that your X Clients display on your Windows desktop.
The ESX server product actually goes one step further than the GSX package, and actually runs below any and all operating systems, removing the waste of resources represented by running a host OS.