You place a order to a retail vendor. The vendor then calls their supllier (JWT, Tire Rack, whoever) and orders the part - rather then having the supplier mail the part to the vendor so that they can in turn mail it to you, drop shipping means that the supplier mails the part directly to the end customer after the vendor places the order w. them. Usually the supplier will even print out a shipping sticker w. the vendors name so that the end customer doesn't even realize it happened.
The advantage when it works well is that the vendor can carry less inventory on hand but can save a little on avoiding the 2 step shipping of parts.