Another thing:
Hamachi is needed only if you have a dynamic IP: when you connect to the internet, your provider assigns to your pc an IP address (another number in the form xxx.xxx.xxx.xxx) which typically varies over time. In order to play Minecraft with your friends, however, you have to use static ip addresses otherwise you coudn't reach the other players. Just imagine to send a mail to a person whose address changes every hour. It's impossible unless there's someone who tells you where is gone your friend. If your ip address never changed you could just tell that ip address to your friends to play together.
Hamachi keeps track of your dynamic ip address and assigns you a "label" (the hamachi virtual ip address) and tells this address to the other PCs participating to the net.