The contact information is a dialog window that can give you more information about a contact. The information in the window is based on the times both you and your contact were online, and it is stored by Plus! (so it will 'start counting' from the moment you install Plus!).
The last seen time is the time you have last seen your contact online. This means that if your contact was online after that, but you were not online, you will not see that he has been online later. The time shown can be read as '... ago': if it says three days, it was three days ago that you saw him online. The same thing is valid for the last conversation time.
There is no difference between viewing this information when a contact is offline or online; the last conversation time will not be affected by this, but of course, when your contact is online, you'll see a different 'last seen online' time
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