A Like button is only for a specific URL. There is no way to 'group' Like clicks together into one larger count. Those URLs can be your Facebook Page or each URL on your site.
So, when a user clicks the Like button on a page of your site, their like will be counted toward that URL only. You can create a JFBCLike module and point it to your Facebook Page if you want. If you leave the URL blank or use the content plugin to automatically put the Like button on your articles, it will be for that page only.
Hope that explains, but if not, let me know!
Thanks,
Alex