A game engine is the framework which is used to lay the groundwork for game developers by providing them with the systems and tools needed like rendering, audio management, level editing, input detection, etc.
In some cases you may find that one game shares the same engine as another. This usually happens due to a company licensing out their engine to be used by a development team or in the case of an in-house engine may not need to make a whole new engine for a game if the one they have works fine. This can lead to file formats being similar or even identical between games which can be useful when it comes to ripping and modding.
Common Engines
In-House Engines