Take for example, Wine. Wine is a program that runs on the Linux operating system. Wine allows the user to run Windows applications designed for Windows on the Linux operating system. If the user did not have Wine, he would not be able to run windows programs. So you can guess that emulators for games act like the console systems which can run games.
Many emulators exist today.
There are probably over a 1000 different emulators out there. Of all these emulators, there are only a few that will actually run the games properly and quickly. Bleem and PS Emu Pro run Playstation games on the computer. Because emulators are programs and not actually the consoles, not all games are supported and sometimes there are minor or major glitches in the programs. But the good part is since they are programs and not restricted to hardware design, they can be updated with fixes and patches that will allow them to run better and give them functions that the consoles do not even have.