spooky,
The Arduino web site Reference section lists functions specific to the Arduino platform. There is also a large suite of generic functions available. Documentation for those functions is at avr-libc: Modules. Those generic functions are the same functions that you'll find with most C compilers.
Will that information provide you with everything that is needed to build a solid understanding of the programming on the Arduino web site? No, but it's a start. You'll also need to understand the C (and, to a lesser extent the C++) programming languages.
Regards,
-Mike