So, I went to localbitcoin, I met a random guy at a Starbucks gave him the money and he transfered 1BTC with his cellphone to my blockchain.info account. I thought I would have to wait at very least 10 minutes or so before the transaction would get included in the blockchain and have the first confirmation, instead the guy sent it and literally one second after that the bitcoin was there in my blockchain.info wallet, how is that possible?
New transactions propagate across the Bitcoin peer-to-peer network very quickly. This is how they get to miners to be included in the block chain (confirmed), but everyone else sees them right away also. Your web wallet software alerted you that it saw a transaction sending 1BTC to your wallet, and updated your balance accordingly, on the assumption that the transaction will eventually be confirmed. But it should also have indicated that the transaction was not yet confirmed, with a message like "unconfirmed" or "0 confirmations". Seeing this, you could decide whether you're willing to let the other guy leave, or if you want him to stick around until the transaction has one or more confirmations.
Of course, it's also possible that you were lucky and a miner found a block very quickly after receiving your transaction. In that case it might actually have been confirmed by the time you saw it.