That's the total time you have been online.
"Total time logged in: 588 days" does not mean that you've a been a member of bitcointalk for 588 days. It means that the total time you have been online is 588*24 hours.
Online in what sense? Even when the computer's off I'm still logged in. And a computer is usually on doing something even if I'm nowhere near it.
Does that 588 days consist only of active scrolling and writing on the forum? I kind of hope not.
It's the time you have spent on bitcointalk.
Whenever your status is "online" that time is increasing. Your status becomes "offline" shortly after you no longer open any new pages.