VMware is a developer of virtualisation software. The name "VMware" comes from the acronym "VM", meaning "virtual machine", while ware comes from second part of "software".
VMware's desktop software runs on Microsoft Windows, Linux, and Mac OS X. VMware's enterprise software, VMware ESX Server, runs directly on server hardware without requiring an additional underlying operating system. With this software you can then again virtually boot up and run an operating system.
The three rounded squares in the logo represent the different virtual machines that VMware can run simultaneously.