Used in business to describe communication outside of the normal channel, or defered to a later time.
Durind a discussion with a large group of people, an issue may be "taken offline" so that it can be discussed by a smaller group of people at a later time.
The act of signing offline immediately upon being sent an instant message by someone you don't want to talk to. This can also be done abruptly in the middle of a convo as if to say "piss off, I'm done".
Dude #1: "Yo, that really annoying chick is IMing me again! what should i say?"
Our team was online and ready. We went to their base, and destroyed everything using rockets and explosive ammo. They were all offline. We stole or destroyed absolutely everything, and offlined them real good!