I'm new to BitCoin, and as I'm doing my adventure, found a site and gave me some micro BitCoins to test and see how the system works. Now, I finally received a message in my Transactions in my Wallet and it was marked with a '?' in front of the message. Hovering over it showed that 0 of 6 verifications. So, do I need to verify the message? When I opened the menu on File, I saw it has a verify message option.
There is nothing you need to do to get your 6 verifications but wait. Approximately every 10 minutes, a new block will be solved that should include your transaction. Once your transaction is in a block, your client will show 1 of 6 verifications. Now you simply need to wait until 5 more blocks are solved. Once this happens, your client will no longer show the ? next to the transaction.
There are two distinct concepts here, confirmation and message verification.
Confirmation is a process by which transactions are confirmed as authentic and permanent by miners on the Bitcoin network. Once a transaction is made, it will automatically accumulate confirmations over time without any further action on your part (and the the number you see when you hover over the transaction will increase). The time required for each confirmation is random, but designed to average about 10 minutes. 6 confirmations is considered to be sufficient to essentially eliminate the risk that the transaction could be invalidated by a so-called double-spend attack.
Message verification is a more specialized feature of Bitcoin, whereby a user can sign a message proving that she is the owner of a particular address, and other users can verify this. It is useful for certain specific applications, but isn't needed to send and receive ordinary transactions.
A good source for information about all these concepts is https://bitcoin.it.