Game engine
Also said as Engine
The reusable software under a game: the parts that draw, play sound, read input, simulate physics and load files. The game itself is the rules and content built on top.
Nobody can afford to rewrite all of that for every game. Picking an engine also picks what is easy and what is a fight, so it is really a design decision.
Say it
“Use Godot for this. It is a 2D game with few characters, so we do not need Unreal's renderer, and the small download matters more than any feature we would give up.”
Where you’ve seen it
id Software kept Doom's code apart from its data, and licensed the Doom engine out: Heretic, Hexen and Strife are all different games on the same one.
Not to be confused with framework
A framework gives you pieces and you write the loop. An engine runs the loop and calls you, and it usually comes with an editor and an asset pipeline.