Items that are bound to you can't be traded, mailed, or auctioned to anyone else. However, you can still sell them at a vendor for money. If you drag a bound item out to try and drop it, a window pops up asking you if you want to destroy the item. Some rare items need you to type "destroy" as an additional confirmation that you indeed want to destroy that item.
Bound items usually come from bosses in higher level dungeons, and they will bind to you as soon as you pick them up, even though you can often trade them with eligible group members for five minutes. Eligible group members are those that were on the map when the boss died - it does not matter whether they were knocked out or not. However, if they were not on the map when the boss died, they are not eligible and you cannot trade, or mail them the item, nor will they be able to pick it up if you drop it.
In addition, most equipment will bind when you first use it. Quest items are also bound to you. Finally, if your group uses loot pool to distribute loot, and you hit "Want" on an item (which bypasses regular roles), the item will bind to you, even if it would normally not.
In order to check to see whether an item is bound to you, scroll over it and look under "Condition" or "# left in your bag" and above the small description of the item in white letters. If an item is not bound to you, nothing will be there. If an item will bind when you first use or equip it, the tooltip will read "Bind on Use" or "Bind on Equip". If an item is already bound to you, it will simply state "Bound".
There is no way to "unbind" items.