An emulator is a software application, usually running on a regular PC computer, which creates a virtual environment resembling another piece of technology inside of which software applications/games designed to run on that second piece of technology can run as if they were running on that second piece of technology.
Usually this means that the machine running the emulator has to be a few orders of magnitude more powerful than the piece of technology being emulated. A Pentium 4 2.4Ghz machine easily emulates a 386 PC running MSDOS from the early 1990s, but oddly enough may still not be powerful enough to emulate a dedicated arcade game console from 2000, designed to run practically live-action arcade games.
There are emulators designed to be run on PC computers, which create environments such as older PCs running MSDOS (DOSBOX), arcade game machines (Multi-Arcade Machine Emulator), and even console environments such as Playstations and XBoxes.
Note that an emulator application creates an entire environment, a "sandbox", inside which the second piece of technology's applications run without ever leaving the "sandbox". There are software applications which allow the running of non-native applications without emulating an entire environment, such as Linux's WINE (Wine Is Not an Emulator) which allows Windows applications to run in Linux without creating an entire Windows environment for the application in which to run.