What C stands for is it was actually the 3rd generation of a series of developmental languages. Don't laugh to much, but they were labeled A, B, and finally C. If you dig (Google and do a lot of searching), you can find compilers for A and B though they are mostly for historical and amusement purposes.
Originally C, and A and B before that, were created for developing operating systems. The idea was to create an easily portable compiler that was also easy to implement in assembly language to help bootstrap new computer operating systems. As it turns out, C is an ideal programming language for a lot of things.because it isn't assembly language, but it can create compiled programs that are very nearly as efficient as assembly language. The simplicity of the language and it's portability made it the first cross platform programming languages.
I should probably include a historical reference to K&R C as it is the older version of C before the C standard was developed. There has been several versions in just the C family. Even in it's K&R form, it was then the most portable programming language available. You can still occasionally find source code written in K&R C and it may cause some problems with modern compilers while some of the older compilers may not have trouble with it. The syntax differences will look a bit strange to anyone who only knows the modern C standard syntax.
Next in history after C is C++. This is an object oriented version of C on steroids. It is best described as a super set of C because so much was added while still being compatible with C. If you know C, then you already know the basics of C++. With some study, you can add the new features and enhancements of C++ and it's object oriented additions.
There should also probably be another historical side note for objective C. An object oriented version of C that isn't C++. Not nearly as popular as C++ or C, you'll occasionally see some questions pop up in Yahoo answers. Objective C is mostly limited to *nix/Linux and possibly Gnu compilers.
Finally, you have C# This is actually a restricted version of C++. I've had friends of mine describe C# as being C++ without the ability to do a lot of harm to the operating system. Microsoft decided that while C++ was good, there was to many ways for programmers to make serious mistakes. The result was C#. Many of the "problems" with C++ have been removed from the programming language while still retaining the object oriented programming feature.
C, C++ and C# can all be used as game programming languages. Your choice may depend on what platform you develop your game for. C# is strictly limited to Microsoft and few are jumping on the bandwagon since you can do the same things with C++ without the restrictions of C#. As far as I know, the only C# compilers are available from Microsoft. C is the base programming language used for Linux (most of the operating system) and newer things for Linux may be written in C++.
If you need more information I suggest Wiki and Google. I've included enough general info here that should enable you to dig a lot deeper if you want to know more.
Shadow Wolf