The buddy list is used to keep track of the friends you have made on this forum. By clicking "Quick Links" ... "Open Buddy List"... you'll be able to see which of your friends are currently online, and be able to send them a private message. Adding people to your buddy list also allow you to send private messages to multiple forum members at the same time. You may add any member of the forums to your buddy list by clicking this button in a member's posts.
Ignore lists are used for those people who's messages you wish not to read. By adding someone to your ignore list, those messages posted by these individuals will be hidden when you read a thread.