What does it mean to write to stdout in C?

That means that you are printing output on the main output device for the session... whatever that may be. The user's console, a tty session, a file or who knows what. What that device may be varies depending on how the program is being run and from where.

The following command will write to the standard output device (stdout)...

printf( "hello world\n" );

Which is just another way, in essence, of doing this...

fprintf( stdout, "hello world\n" );

In which case stdout is a pointer to a FILE stream that represents the default output device for the application. You could also use

fprintf( stderr, "that didn't go well\n" );

in which case you would be sending the output to the standard error output device for the application which may, or may not, be the same as stdout -- as with stdout, stderr is a pointer to a FILE stream representing the default output device for error messages.

It depends.

When you commit to sending output to stdout, you're basically leaving it up to the user to decide where that output should go.

If you use printf(...) (or the equivalent fprintf(stdout, ...)), you're sending the output to stdout, but where that actually ends up can depend on how I invoke your program.

If I launch your program from my console like this, I'll see output on my console:

$ prog
Hello, World! # <-- output is here on my console

However, I might launch the program like this, producing no output on the console:

$ prog > hello.txt

but I would now have a file "hello.txt" with the text "Hello, World!" inside, thanks to the shell's redirection feature.

Who knows – I might even hook up some other device and the output could go there. The point is that when you decide to print to stdout (e.g. by using printf()), then you won't exactly know where it will go until you see how the process is launched or used.