ヘッダーファイルは、繰り返さないように使用されます。あなたの例では、書く必要はありませんでした
extern int one;
でheadertest2.c、ヘッダーファイルを介してそのファイルにすでに含まれているためです。
繰り返さないことは小さなことではありません。このグローバル変数（one）を使用するファイルが100個あるとします。それらすべてを書きたいextern int oneですか？これらの変数が20個あり、さらに50個の関数がある場合はどうなりますか？に変更したい場合はどうなりますか？intuint32_t
確かに、定義を複製するのは面倒でエラーが発生しやすいです。
stdio.hたとえば見てみましょう。ヘッダーがないと、I/Oを実行するすべてのファイルに次のコードをコピーして貼り付ける必要があります。
/* Define ISO C stdio on top of C++ iostreams.
Copyright (C) 1991, 1994-2008, 2009, 2010 Free Software Foundation, Inc.
This file is part of the GNU C Library.
The GNU C Library is free software; you can redistribute it and/or
modify it under the terms of the GNU Lesser General Public
License as published by the Free Software Foundation; either
version 2.1 of the License, or (at your option) any later version.
The GNU C Library is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
Lesser General Public License for more details.
You should have received a copy of the GNU Lesser General Public
License along with the GNU C Library; if not, write to the Free
Software Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA
02111-1307 USA. */
/*
* ISO C99 Standard: 7.19 Input/output <stdio.h>
*/
#ifndef _STDIO_H
#if !defined __need_FILE && !defined __need___FILE
# define _STDIO_H 1
# include <features.h>
__BEGIN_DECLS
# define __need_size_t
# define __need_NULL
# include <stddef.h>
# include <bits/types.h>
# define __need_FILE
# define __need___FILE
#endif /* Don't need FILE. */
#if !defined __FILE_defined && defined __need_FILE
/* Define outside of namespace so the C++ is happy. */
struct _IO_FILE;
__BEGIN_NAMESPACE_STD
/* The opaque type of streams. This is the definition used elsewhere. */
typedef struct _IO_FILE FILE;
__END_NAMESPACE_STD
#if defined __USE_LARGEFILE64 || defined __USE_SVID || defined __USE_POSIX \
|| defined __USE_BSD || defined __USE_ISOC99 || defined __USE_XOPEN \
|| defined __USE_POSIX2
__USING_NAMESPACE_STD(FILE)
#endif
# define __FILE_defined 1
#endif /* FILE not defined. */
#undef __need_FILE
#if !defined ____FILE_defined && defined __need___FILE
/* The opaque type of streams. This is the definition used elsewhere. */
typedef struct _IO_FILE __FILE;
# define ____FILE_defined 1
#endif /* __FILE not defined. */
#undef __need___FILE
#ifdef _STDIO_H
#define _STDIO_USES_IOSTREAM
#include <libio.h>
#if defined __USE_XOPEN || defined __USE_XOPEN2K8
# ifdef __GNUC__
# ifndef _VA_LIST_DEFINED
typedef _G_va_list va_list;
# define _VA_LIST_DEFINED
# endif
# else
# include <stdarg.h>
# endif
#endif
#ifdef __USE_XOPEN2K8
# ifndef __off_t_defined
# ifndef __USE_FILE_OFFSET64
typedef __off_t off_t;
# else
typedef __off64_t off_t;
# endif
# define __off_t_defined
# endif
# if defined __USE_LARGEFILE64 && !defined __off64_t_defined
typedef __off64_t off64_t;
# define __off64_t_defined
# endif
# ifndef __ssize_t_defined
typedef __ssize_t ssize_t;
# define __ssize_t_defined
# endif
#endif
/* The type of the second argument to `fgetpos' and `fsetpos'. */
__BEGIN_NAMESPACE_STD
#ifndef __USE_FILE_OFFSET64
typedef _G_fpos_t fpos_t;
#else
typedef _G_fpos64_t fpos_t;
#endif
__END_NAMESPACE_STD
#ifdef __USE_LARGEFILE64
typedef _G_fpos64_t fpos64_t;
#endif
/* The possibilities for the third argument to `setvbuf'. */
#define _IOFBF 0 /* Fully buffered. */
#define _IOLBF 1 /* Line buffered. */
#define _IONBF 2 /* No buffering. */
/* Default buffer size. */
#ifndef BUFSIZ
# define BUFSIZ _IO_BUFSIZ
#endif
/* End of file character.
Some things throughout the library rely on this being -1. */
#ifndef EOF
# define EOF (-1)
#endif
/* The possibilities for the third argument to `fseek'.
These values should not be changed. */
#define SEEK_SET 0 /* Seek from beginning of file. */
#define SEEK_CUR 1 /* Seek from current position. */
#define SEEK_END 2 /* Seek from end of file. */
#if defined __USE_SVID || defined __USE_XOPEN
/* Default path prefix for `tempnam' and `tmpnam'. */
# define P_tmpdir "/tmp"
#endif
/* Get the values:
L_tmpnam How long an array of chars must be to be passed to `tmpnam'.
TMP_MAX The minimum number of unique filenames generated by tmpnam
(and tempnam when it uses tmpnam's name space),
or tempnam (the two are separate).
L_ctermid How long an array to pass to `ctermid'.
L_cuserid How long an array to pass to `cuserid'.
FOPEN_MAX Minimum number of files that can be open at once.
FILENAME_MAX Maximum length of a filename. */
#include <bits/stdio_lim.h>
/* Standard streams. */
extern struct _IO_FILE *stdin; /* Standard input stream. */
extern struct _IO_FILE *stdout; /* Standard output stream. */
extern struct _IO_FILE *stderr; /* Standard error output stream. */
/* C89/C99 say they're macros. Make them happy. */
#define stdin stdin
#define stdout stdout
#define stderr stderr
__BEGIN_NAMESPACE_STD
/* Remove file FILENAME. */
extern int remove (__const char *__filename) __THROW;
/* Rename file OLD to NEW. */
extern int rename (__const char *__old, __const char *__new) __THROW;
__END_NAMESPACE_STD
#ifdef __USE_ATFILE
/* Rename file OLD relative to OLDFD to NEW relative to NEWFD. */
extern int renameat (int __oldfd, __const char *__old, int __newfd,
__const char *__new) __THROW;
#endif
__BEGIN_NAMESPACE_STD
/* Create a temporary file and open it read/write.
This function is a possible cancellation points and therefore not
marked with __THROW. */
#ifndef __USE_FILE_OFFSET64
extern FILE *tmpfile (void) __wur;
#else
# ifdef __REDIRECT
extern FILE *__REDIRECT (tmpfile, (void), tmpfile64) __wur;
# else
# define tmpfile tmpfile64
# endif
#endif
#ifdef __USE_LARGEFILE64
extern FILE *tmpfile64 (void) __wur;
#endif
/* Generate a temporary filename. */
extern char *tmpnam (char *__s) __THROW __wur;
__END_NAMESPACE_STD
#ifdef __USE_MISC
/* This is the reentrant variant of `tmpnam'. The only difference is
that it does not allow S to be NULL. */
extern char *tmpnam_r (char *__s) __THROW __wur;
#endif
#error Omitted due to post length limit
__BEGIN_NAMESPACE_STD
#ifndef __USE_FILE_OFFSET64
/* Get STREAM's position.
This function is a possible cancellation point and therefore not
marked with __THROW. */
extern int fgetpos (FILE *__restrict __stream, fpos_t *__restrict __pos);
/* Set STREAM's position.
This function is a possible cancellation point and therefore not
marked with __THROW. */
extern int fsetpos (FILE *__stream, __const fpos_t *__pos);
#else
# ifdef __REDIRECT
extern int __REDIRECT (fgetpos, (FILE *__restrict __stream,
fpos_t *__restrict __pos), fgetpos64);
extern int __REDIRECT (fsetpos,
(FILE *__stream, __const fpos_t *__pos), fsetpos64);
# else
# define fgetpos fgetpos64
# define fsetpos fsetpos64
# endif
#endif
__END_NAMESPACE_STD
#ifdef __USE_LARGEFILE64
extern int fseeko64 (FILE *__stream, __off64_t __off, int __whence);
extern __off64_t ftello64 (FILE *__stream) __wur;
extern int fgetpos64 (FILE *__restrict __stream, fpos64_t *__restrict __pos);
extern int fsetpos64 (FILE *__stream, __const fpos64_t *__pos);
#endif
__BEGIN_NAMESPACE_STD
/* Clear the error and EOF indicators for STREAM. */
extern void clearerr (FILE *__stream) __THROW;
/* Return the EOF indicator for STREAM. */
extern int feof (FILE *__stream) __THROW __wur;
/* Return the error indicator for STREAM. */
extern int ferror (FILE *__stream) __THROW __wur;
__END_NAMESPACE_STD
#ifdef __USE_MISC
/* Faster versions when locking is not required. */
extern void clearerr_unlocked (FILE *__stream) __THROW;
extern int feof_unlocked (FILE *__stream) __THROW __wur;
extern int ferror_unlocked (FILE *__stream) __THROW __wur;
#endif
__BEGIN_NAMESPACE_STD
/* Print a message describing the meaning of the value of errno.
This function is a possible cancellation point and therefore not
marked with __THROW. */
extern void perror (__const char *__s);
__END_NAMESPACE_STD
/* Provide the declarations for `sys_errlist' and `sys_nerr' if they
are available on this system. Even if available, these variables
should not be used directly. The `strerror' function provides
all the necessary functionality. */
#include <bits/sys_errlist.h>
#ifdef __USE_POSIX
/* Return the system file descriptor for STREAM. */
extern int fileno (FILE *__stream) __THROW __wur;
#endif /* Use POSIX. */
#ifdef __USE_MISC
/* Faster version when locking is not required. */
extern int fileno_unlocked (FILE *__stream) __THROW __wur;
#endif
#if (defined __USE_POSIX2 || defined __USE_SVID || defined __USE_BSD || \
defined __USE_MISC)
/* Create a new stream connected to a pipe running the given command.
This function is a possible cancellation point and therefore not
marked with __THROW. */
extern FILE *popen (__const char *__command, __const char *__modes) __wur;
/* Close a stream opened by popen and return the status of its child.
This function is a possible cancellation point and therefore not
marked with __THROW. */
extern int pclose (FILE *__stream);
#endif
#ifdef __USE_POSIX
/* Return the name of the controlling terminal. */
extern char *ctermid (char *__s) __THROW;
#endif /* Use POSIX. */
#ifdef __USE_XOPEN
/* Return the name of the current user. */
extern char *cuserid (char *__s);
#endif /* Use X/Open, but not issue 6. */
#ifdef __USE_GNU
struct obstack; /* See <obstack.h>. */
/* Write formatted output to an obstack. */
extern int obstack_printf (struct obstack *__restrict __obstack,
__const char *__restrict __format, ...)
__THROW __attribute__ ((__format__ (__printf__, 2, 3)));
extern int obstack_vprintf (struct obstack *__restrict __obstack,
__const char *__restrict __format,
_G_va_list __args)
__THROW __attribute__ ((__format__ (__printf__, 2, 0)));
#endif /* Use GNU. */
#if defined __USE_POSIX || defined __USE_MISC
/* These are defined in POSIX.1:1996. */
/* Acquire ownership of STREAM. */
extern void flockfile (FILE *__stream) __THROW;
/* Try to acquire ownership of STREAM but do not block if it is not
possible. */
extern int ftrylockfile (FILE *__stream) __THROW __wur;
/* Relinquish the ownership granted for STREAM. */
extern void funlockfile (FILE *__stream) __THROW;
#endif /* POSIX || misc */
#if defined __USE_XOPEN && !defined __USE_XOPEN2K && !defined __USE_GNU
/* The X/Open standard requires some functions and variables to be
declared here which do not belong into this header. But we have to
follow. In GNU mode we don't do this nonsense. */
# define __need_getopt
# include <getopt.h>
#endif /* X/Open, but not issue 6 and not for GNU. */
/* If we are compiling with optimizing read this file. It contains
several optimizing inline functions and macros. */
#ifdef __USE_EXTERN_INLINES
# include <bits/stdio.h>
#endif
#if __USE_FORTIFY_LEVEL > 0 && defined __extern_always_inline
# include <bits/stdio2.h>
#endif
#ifdef __LDBL_COMPAT
# include <bits/stdio-ldbl.h>
#endif
__END_DECLS
#endif /* <stdio.h> included. */
#endif /* !_STDIO_H */
それが、ヘッダーファイルがある理由です。