A scripting language is a programming language that allows scripts to be written for it. A script is a program that can be executed without being compiled in one of a few different ways. Scripting languages are also sometimes referred to as very high-level programming languages, as they operate at a high level of abstraction, being very fast to learn how to write in.
Scripting languages also have the advantage of taking care of a lot of things that programmers would need to take care of, such as garbage collection, memory management, and pointers, which often confuse non-developers. Even a visual editor such as Unreal 4's blueprints is still a scripting language, as it accomplishes the same thing as a written one does.
Most games use scripting languages in some form, but other games may use it a lot more, such as how GameMaker uses Game Maker Language (GML) for their logic.