NLua is a .NET library that allows you to easily integrate Lua in your C# application, calling Lua functions, reading Lua tables or calling C# methods from within Lua scripts. NLua is actually a fork of the project called LuaInterface from Craig Presti/Fabio Mascarenhas so most of features and documentation you find from LuaInterface
should work with NLua.
You could use Lua to script parts of your application, allowing to quickly change behavior without having to rebuild your application. Scenarios like games, customization, extensions.