The blacklist is a means to block the appearance and activity of players that have verbally harassed you or otherwise harmed you in any way. There are two blacklists; the chat blacklist and the character blacklist. The chat blacklist is accessible through the options window, however it only blocks chat. The character blacklist blocks both the avatar and their chat.
When you add a character to your blacklist, the client will automatically block out the specific character so that you will never see them in-game or hear them speak.
To add a character to your blacklist, simply right-click their avatar and select 'Add to Blacklist'. The blacklist can be found at the bottom of your friends list. Names can be removed from the blacklist from here.
Blacklisted people are still able to see you if they have not added you to their blacklist.
If you add people to your blacklist, and your friends list is full, they will not be added to the blacklist section of your friends list, though you will then have to log out and then log back to see them again. Also, if you are seated on a mount after you add them to your blacklist, your character will appear to float on air.