What is a game engine anyway?

A game engine is analogous to a car engine: the game engine is what drives the game. You will tell the engine what you want, and (using C++ code and the UE4 editor) the engine will be responsible for actually making that happen.

You will build your game around the UE4 game engine, similar to how the body and wheels are built around an actual car engine. When you ship a game with UE4, you are basically customizing the UE4 engine and retrofitting it with your own game's graphics, sounds, and code.