How do header and source files in C work?

I've perused the possible duplicates, however none of the answers there are sinking in.

tl;dr: How are source and header files related in C? Do projects sort out declaration/definition dependencies implicitly at build time?

I'm trying to understand how the compiler understands the relationship between .c and .h files.

Given these files:

header.h:

int returnSeven(void);

source.c:

int returnSeven(void){
    return 7;
}

main.c:

#include <stdio.h>
#include <stdlib.h>
#include "header.h"
int main(void){
    printf("%d", returnSeven());
    return 0;
}

Will this mess compile? I'm currently doing my work in NetBeans 7.0 with gcc from Cygwin which automates much of the build task. When a project is compiled will the project files involved sort out this implicit inclusion of source.c based on the declarations in header.h?