A game engine is a software framework designed for the creation and development of video games. Developers use them to create games for consoles, mobile devices and personal computers. 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, localization support, scene graph, and may include video support for cinematics. The process of game development is often economized, in large part, by reusing/adapting the same game engine to create different games,[1] or to make it easier to "port" games to multiple platforms. (source: Wikipedia)

Game engines are supposed to make game development easier by providing all these tools and features that developers can just "use" out of the box and don't need to create themselves for every new game. There is though some learning curve to get familiar with functions and scripting in different engines. I also think that these "universal" engines also have multiple programming-language support for developers from different programming languages to be able to program the same game and avoid the learning curve of each programming language.

I just played with these engines a bit, created few 2d games myself following tutorials but I don't really have time to start thinking about serious game programming since I'm involved in completely different area in college.

I personally was trying out unity engine but there are also other engines like source 2 from Valve and Unreal engine.

Whether it's more fun to develop a game or to play a game depends on every person. I personally enjoy in both but I never did game development professionally so I cannot tell about that or how to even begin planning on your own game projects.

Best regard and good luck! :)