A Hackintosh PC, as the name would suggest, is a vanilla PC running a hacked version of Apple’s Mac OS X operating system.
OS X is specifically designed to run on Apple’s hardware line: a Hackintosh is simply non-Apple hardware using the operating system.
Although Apple opposes the practice of hijacking their OS for use on off-brand PCs, many technology-oriented people who don’t want to buy the hardware from Apple choose to spend a lot of time and effort in creating a Hackintosh.