Also, the recipient needs to be synced up with the block chain before it'll see the received transaction. That means the status bar at the bottom needs to say at least 33000 blocks, like "x connections 33200 blocks x transactions".
The number of blocks of a transaction is the amount of new blocks that have been generated by the whole network after the transaction. Each new block in the chain means new coins to its creator. One "generated" -transaction in your transaction list means that you have generated one block. You're not the first one to find the concept of a "block" a bit confusing on the first sight.
Would it be clearer if the status said "x confirmations", like:
Each block essentially means another node has confirmed that it agrees with all transactions up to that point.