A game engine contains all the common tools used to make video games. Among the bigger components are - graphics/rendering engine, which draws the game world onto the screen in real time; a physics engine, which simulates real world physics for objects in the game, including detecting collisions; and other software-related modules that are commonly needed by games, like a domain specific scripting, asset (textures, levels, etc) management, networking, etc.

These are typically things needed by most games. If a developer didn’t use a game engine they’d have to code it specifically for the game. For example if you wanted to write a game without using a pre-canned rendering engine you’d have to figure out the graphics math, communicate with GPU, and optimize for running in real-time.

If the innovative feature of a game is unrelated to any of the standard components, it usually is beneficial to just pick an engine off the shelf (and pay licensing fees). This is why a lot of modern games look and feel the same these days; they get to reuse the basics and really invest into the idea that makes that game unique. It’s only rarely that a game requires a totally different renderer or totally different physics engine.