ELI5: What exactly is a game engine?

Hello. I have been wondering this for a while and I thought this may be a good place to ask. I am always reading about game engines, you know like Frostbite, Unreal, Gamebryo, Snowdrop...etc. I have always wondered what exactly a game engine is and what does it do.

Is a game engine something that developers create themselves or is it created by an outside source? Are they created or modified for specific games? What does it provide, like animations, lighting, physics...etc?

I am sure there are more questions that I have, but I will stop as I think you have the idea.

Thank you in advance for your responses!