The Drop trick is a process of getting multiples of an item that is otherwise restricted to having only one copy. For example, the Anti dragon breath shield: talking to the Duke of Lumbridge gets the player one shield, and he won't give any more after that. However, if the player drops the shield and asks for another one, he will give it. The player can repeat this process as many times as they want, and pick all the shields up off the ground when the player is done. This allows the player to gain as many anti dragon breath shields as they want.
This technique is used with many quest items that players want more of, either because they have benefits useful outside of the quest, to speed up the quest in case they lose something important along the way, or just to retain a copy.