Transactions with "0 confirmations" are transactions that your client has seen, but haven't been put into a block yet.
Here's what happened when you bought the bitcoins:
Seller: "Hey Bitcoin Network! These here Bitcoins are getting sent to that there Bitcoin Address!"
Your client, listening in on all the payment network messages: "Wow, spiffy, that's one of MY Bicoin Addresses! I'll add that transaction to my wallet, and show that transaction as 0/unconfirmed in the UI."
Then your client goes on its merry way downloading the 66,241 blocks in the block chain.
In the meantime, some lucky soul generates block number 66,242, and includes your transaction in that block. When your client connects that block up to the block chain (which it won't do until it gets all 64,241 previous blocks), it'll show it as "1/unconfirmed"
Then 2 confirmations when block 66,243 gets generated, etc.
Wonky things can happen if two nodes generate a different block 66,241 (especially if one of them included your transaction and one of them didn't, you can go from 1/unconfirmed back to 0/unconfirmed for a little while), but after a couple more blocks get generated everything sorts itself out.