From Diablo Wiki
Drop in Diablo II
In Diablo II, a monster will activate the "drop" animation of whatever items they were randomly assigned to give off when killed. This is a term that is used not only in Diablo II but in many other RPGs.
When an item "drops" in Diablo II, any player in the game can pick it up, which can be a source of some conflict.
This was also a term used by players trading, since a player needed to drop the item on the floor in order to show the stats to others.
Drop in Diablo III
In Diablo III, items will again drop on the floor, but each player will have his or her own set of drops. Other players drops will be invisible. In order to give an item to another player, it must be picked up, and then manually dropped or traded.