A compiler is the program which takes the code you write and translates it into machine-readable code. In essence, it turns C code into executable and .dll files.
Writing in C is not easy, nor in any code. One needs more than just a compiler, but to learn the language, one needs a compiler anyway. Microsoft offer a range of free compiler tools known as the "Visual Studio" series, the free variants being dubbed "Express Edition" for a particular language. So, to code in C++, which is the language of Orbiter addons and native windows applications, you would get a C++ compiler, for instance, Visual C++ 2010 Express Edition, available
here.
Note that while the tools provided by Microsoft are free at the Express Edition level, they do require registration after 30 days. There are many other compilers out there, as well, and one can get lost in the myre of differing programs, which is why I suggest only one.
Also, the MSDN offers tutorials for writing in C and C++, available from within the IDE (Integrated Development Environment) after installation.
Good luck with it.