The header files belonging to a standard C environment are usually placed in /usr/include/.. directories. They are referenced from within a C file using < and > brackets. The following lists popular header files and what they contain.
Macros and type declarations
access to environment, memory allocation (malloc..), utilities
Streaming input and output of characters
String function prototypes
Character handling (upper/lower case, alpha/numeric etc.)
wide characters for internationalization (I18n) and localization
like ctype only for wide characters
says how big integer types are on THIS platform
implementation limits for floating-point numbers
math functions
diagnose problems using assert statements
many error codes. check it if you receive an error code from a program
important functions and constants for localization of programs (language codes, message catalog functions)
support for functions with variable arguments
run-time exceptions sent by the kernel
Usually there are also system related include files under /usr/include/sys which contain device descriptions, kernel structure descriptions etc.
These header files list a lot of function prototypes. Those prototypes are program code (object code) and NOT contained in the header files. They are only declared there. The functions themselves live in libraries which can be found under /usr/lib on many platforms.