The HTML file with the "#include" in it needs the .shtml extension. The included file can have, as far as I know, any extension that you'd like.
Do you have the line:
in your .htaccess file for that folder?
The comment marks perform two functions:
1. They identify the line as an 'include' directive. You can think of the "<!--" as part of the "#include".
2. They prevent the actual text of the line from being shown by the browser if the file doesn't get included for some reason.
If I'm recalling things correctly, you can use the .html extension for your pages with includes if you add the line:
to your .htaccess file for that folder.
AddHandler server-parsed .html