If you open the Steam client, then on the top-left of that window are the menus:
Steam, View, Friends, Games, Help.
At the bottom of the Friends menu are the choices: Online, Away, Invisible, Offline.

If you opt for Online or Away then your Profile will show you as Currently Online.
If you opt for Invisible or Offline then your Profile will show Currently Offline
AND how long it's been since you were last Online.

This is the status your avatar will indicate, wherever it is displayed as well.
Invisible is a special status. When set to that, you'll technically be Online but
to everyone else you will appear as Offline.

I hope I haven't gone too overboard in answering your question. :)

Says I am currently offline - and for the past 383 days? Don't know if anyone can read this but what's goin' on?