That means u r signed in from some other place, like your Smartphone, or some IM client like Trillian etc, or u have Facebook Messenger installed on ur phone, due to which u r always online when u sign-in.
Did u use a IM Client like IMO by any chance? Because with IMO, even if u remove it (while ur status was online from IMO client), u r still signed into Facebuk. I eventually had to download it again, sign-in, changed my status to offline. And since then, I haven't faced any issue.