NOTE:
You should no longer use this, but use the modified mono mcs.dll by Jakub Rak instead which is located here -> https://github.com/aeroson/mcs-ICodeCompiler . It is a lot easier to set up and use. I will keep this package available for educational reasons though.
Basic example on how to use CS-Script ( http://www.csscript.net/ ) inside Unity.
With CS-Script you are able to compile and run C# scripts at runtime. This way you can ship new C# code after release without building a new version.
This is also a great start for adding mod support to your game.
See comments inside samplescripts for more info on how it works.
Note:
Compiling C# at runtime will NOT work on iOS as it is permitted by apple (AOT <-> JIT). The same is true for consoles. If you need a runtime script solution which will work on all platforms, you should use a Unity compatible LUA interpreter like http://www.moonsharp.org instead.