The dots (or round buttons) that appear next to every member's name are online status indicators. A green dot means the user is currently online, browsing or posting to the site. A grey/pale-blue dot means that the user is not online, or that the user account is set to "invisible mode" (configurable in the
User CP). A red dot appears only next to your own name, and means that you are online (of course) but in "invisible mode."
A user's status is also listed in his or her profile, and in the site-wide "
Who's Online" list.