Item binding[]
Some items in the game become bound to your character, meaning those items can't be traded or auctioned. Most items can still be sold to a vendor. Some items are bind-on-pickup (BOP) and some are bind-on-equip (BOE). BOE items can be traded or auctioned as long as you don't equip them. BOP items are bound to your character the moment they appear in your inventory. An items tooltip will tell you if it binds and how.
Item unbinding[]
Generally speaking, there is no way to unbind items. Some UI elements referenced unbinding companions early in the game's history, but they did not function and were eventually removed.
In the Profession system, when a task consists of upgrading a piece of armor, it is possible to take a bound item as the ingredient, and have an unbound item as a result, though this is technically a new item.