A embedded script engine is good for fast development, fast modification, fast experiment, and adding some app-specific DSL. E.g. in a C++ game, changing some rules or some config would take a re-compile of the project, deployment, and restart. Moving the game logic, rule, map layout, asset, config, etc, to the embedded script engine would allow immediate changes via reloading of the script while the game is running.

For embedding, you need some small language with small runtime. Something like Scheme/Lisp/Lua would work. Something like Python is not suitable. Lua is popular in the gaming scene because of its small size and its well designed architecture for embedding. Looks like Javascript is getting there.