This is a real noob question but here goes...
How does the offline wallet know about new receiving addresses created on the online computer? The reason I ask is that I clicked the "Receive Bitcoins" button on the online computer and a new receiving address was created. My immediate thought was that the other computer is offline so how is it going to know about the new address and the coins it has received? Will the received coins show in the offline balance? How does this work?
New addresses are created by a formula.
The online and offline computers use the same parameters for that forumula, so they both generate the same sequence of addresses.