I just got a tiny Bitcoin in my wallet that says it was "Generated" 0.00004123.
I thought this new version did not have generating in it any more? Or is this something different from mining that was previously built in to BitCoin client?
Can someone explain why it generated a teeny-weeny BitCoin for me?
This is something different from mining that was previously built into the Bitcoin client.
This just means that you received coins directly from the 50 BTC one receives every time you find a block. If you solo mine, you get a 50 BTC generate transaction every time you find a block. They're also used for payouts on Eligius (likely how you got the small amount).