Anita,
There's a few ways that JFBConnect can post activity to Facebook on a user's behalf. JFBConnect can post 'actions' that a user takes, like reading an article, uploading a photo, voting for content, leaving reviews and other activity on your site from various extensions. These are called Open Graph Actions and aren't actual status updates, but things like "I listened to a song" (from Spotify), only from your site.
If you're using JomSocial, we also have an option to automatically post any status updates a user makes into JomSocial to go directly to Facebook as well on that user's behalf.
Currently, we don't have auto-posting abilities to Twitter. That will be included in an upcoming release.
I hope that helps explain, but if you have any other questions, just let me know.
Thanks,
Alex