Lua is often used as an embedded scripting language within level editors, for example to keep track of the progress made on a quest or to trigger an event when the character reaches a certain point. Lua isn't used to code the game engine itself (in the vast majority of cases, there may be some obscure examples of game engines written in Lua)

Lua is pretty popular because it is a simple scripting language that you can either run in an interpreter, or compile to C. The interpreter is easily embeddable, and you can call C functions from it. All of this makes for pretty rapid development without sacrificing speed for the things that it is suitable for.