Well in general you use a scripting language to customise behaviour of objects within your game. In your RTS example you could have a script for each unit which would define it's behaviour. You could specify what it would do when you tell it attack something, specify its responses to various stimuli (i.e. what does it do if an enemy approaches, a unarmed citizen unit may run, while a tank might shoot). You could use scripts to specify how buildings work as well.

In terms of how you actually use scripts within a programming language the specifics depend upon what language you choose to embed. But normally you'll have some form of API that will allow you to tell the script interpreter to load and run script files, call functions within script files, get/set variables within script files etc. They'll also be API functions to bind function within your program so they can be used within scripts (i.e. in an RTS you could bind a WalkTo function so it can be used within a script, then when say the tank script decides to move the tank somewhere it can use the WalkTo function to do it).

You also mention C#, note that this can be used as a scripting language if you wish.

Because a scripting language will be simpler to program in than C++, you also won't need to recompile everytime you need to make a script change.

Through some clever stuff you can do with the .Net framework you can compile C# code and then call it from your application. There's been a few threads on it see the one here.

Quote:... why not just program all that stuff in C++? ...

Because my level design team don't know C++ (actually, I am my level design team, but that's not the point)
Because I want my end users to be able to make their own maps and rules (suddenly I have a much larger team ;)
Because I don't want to recompile to change one configuration variable.

In your case, say you want to add a new unit with new behaviours to your game. You edit a bunch of sprites so it can be drawn. You edit a data file indicating how it can be constructed in the game, and who by, and how much it costs. You do everything required outside of your code, apart from the bit which indicates what it does, which is a unique, and new, algorithm. If this can be done in script also, it becomes possible to create entire new units with new abilities, even whole new AIs, without access to the source code. It's much tidier that way, and in some ways, it's actually easier to debug aswell. And your game is halfway to being modable.

Having gone to the trouble of adding scripting (I choose game monkey this time round, to see what it's like, and so far it's good) I now use it for everything I need to load. It is possible for a user to write for loops and branch statements in the config file that defines all their keys, which is probably pointless in my case, but required no effort on my part, and in other games would mean a config file could say:

if (class == warrior)    bindkey(x, jump);else    bindkey(x, duck);

or whatever.