What exactly module in D means?

[Andre Tampubolon via Digitalmars-d-learn]

I've been reading the newsgroup for a while, and it seems that one of 
the reason folks like D is because it supports module.

My question is: what does module mean?
A quick google pointed my this page: http://dlang.org/module.html.
Still cannot understand it, though :)

How does it differ from the old C's #include?

For example, consider the hello world in C.

#include <stdio.h>

int main(void){
	printf("%s\n", "Hello world...");
	return 0;
}

The C preprocessor while replace the line "#include <stdio.h>" with the 
content of stdio.h itself.

While in D:

import std.stdio;

void main(){
	writeln("Hello world...");
}

Does that mean the compiler take the "definition" of writeln itself from 
stdio.d and paste it into my program? Pardon my ignorance, because I'm 
not versed in compiler theory.