Lua is a programming language that is lightweight and easy to embed into other software, like games.
The Lua.org web page has this to say:
Lua is a powerful, fast, lightweight, embeddable scripting language.
Lua combines simple procedural syntax with powerful data description constructs based on associative arrays and extensible semantics. Lua is dynamically typed, runs by interpreting bytecode for a register-based virtual machine, and has automatic memory management with incremental garbage collection, making it ideal for configuration, scripting, and rapid prototyping.
To learn how to program Lua, the Lua-users wiki might be a good place to start, or just Google search, "Learning Lua." There are many good, free, online options.