The game engine is what powers the entire game, it keeps track of health, inventory, game progress and other essential stats. If the game has any non-player characters then it handles artificial intelligence, basically a set of rules which define how the environment and other characters interact with the player. It also draws stuff on the screen, handles models, sprites, movement and physics, it plays music and sound effects and deals with keyboard, mouse or gamepad input. Without an engine you have a pile of sounds and pictures, it's basically the code, the glue that holds everything together, the brain of the game.