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.