Lua is a powerful, fast, lightweight, embeddable scripting language. Garry's Mod includes it vanilla and is what most addons are written in; including a good portion of the vanilla tools and entities. If you intend to install addons on to your Garry's Mod server, it is wise to understand the essentials of Lua, and while Garry has included some core libraries for use in the game; the majority of the native Lua functions remain.

Programming In Lua: http://www.lua.org/pil/1.1.html (Step-by-step explanation of the programming langauge)
Garry's Mod Function Documentation: http://wiki.garrysmod.com
Garry's Mod Wikipedia: http://gmod.wikia.com/