This is a definition of a game engine taken from Wikipedia:
"A game engine is a software system designed for the creation and development of video games. There are many game engines that are designed to work on video game consoles and desktop operating systems such as Linux, Mac OS X, and Microsoft Windows. The core functionality typically provided by a game engine includes a rendering engine (“renderer”) for 2D or 3D graphics, a physics engine or collision detection (and collision response), sound, scripting, animation, artificial intelligence, networking, streaming, memory management, threading, and a scene graph. The process of game development is frequently economized by in large part reusing the same game engine to create different games."
This basically translates into what you run your models through to make them playable, or to make the characters playable etc.
I have limited knowledge of game engines, actually id didn’t even know they existed before this course
This explains (almost) basically what a game engine is:
The game engine is generally the library of core functions used in the game, usually related to graphics, input, networking and other systems.
Another explanation of the game engine is taken from this website: http://www.gamecareerguide.com/features/529/what_is_a_game_.php
This extract explains that the game engine is basically the component that brings the game to life i.e. the animating objects/characters, loading screens and displays and "collision detection between objects".
Also according to some of the second/third years and heather the game engine is also where your mistakes when modelling are found, when for example two faces and overlapping etc.