VMWare, from VMware, Inc., is a series of software packages intended to provide virtual machine technology to Windows and Linux; the most commonly used outside of a clustered context are VMWare Workstation, VMWare Server, VMware Fusion, and VMWare ESXi. The former three allow 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. ESXi (Formerly VMware ESX Server) differs in that there is no host operating system, only the ESX Hypervisor.
What makes VMWare special compared to emulation software such as 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. While today there are numerous virtualization options including VirtualBox, Xen, and KVM at the time VMware was delivered (and for years thereafter) it was the only virtualization solution available for x86.
The different types of VMware provide different features, and are targeted at different markets. Workstation is intended mostly for developers and testers, and makes it easy to take multiple snapshots and revert to earlier machine states. Server allows you to easily run multiple virtual servers on a single machine and manage them remotely; the default interface is web-based and works with either Internet Explorer or Firefox. Fusion is a product for the Macintosh (with Mac OS X) which seemingly integrates Windows applications with the Apple system. ESXi is a hypervisor environment which consumes minimal resources, eliminating the host operating system entirely. There are numerous other products as well, but these are those one is most likely to encounter. Server and ESXi are both provided free-as-in-beer even for commercial use, with the hopes that users will find them lacking and move up to an "enterprise-grade" product.