Hello George,
Thank you for your message.
Idle or offline literally means that the computer is either idle (online and ready to accept connections) or offline (meaning that it's offline or even the Host is not installed at all).
You are probably confusing the idle state with the logged in state. The remote Host can be idle and awaiting your connection but you may not have been connected to it yet. In this case it's a grey monitor and the status is "Idle or offline". Then when you log in to that Host using the Login command, you are "explicitly" connected to that Host in which case the icon turns to a green monitor.
This is more read on the subject:
Color codes and statusesLogon/LogoffDon't hesitate to ask me if you have other questions.