Software running in a non-x86 machine (non-PC) that runs applications written for an x86 machine. x86 emulators were first developed to run 16-bit DOS and Windows 3.1 applications, and later, 32-bit Windows applications.
Technically, most x86 emulators are really x86 translators, as they convert the x86 instructions into instructions for the native computer rather than actually simulate the foreign instructions. See x86, Wine and Odin.