An example of a Drag Shot.

Drag Scope or "Drag Shot" is an in-game term commonly associated with Sniper Rifles. Basically, the Drag-Scope is when you scope in and quickly adjust your crosshair to the enemy and then shooting. It is mainly based upon luck*, however it still requires the right timing and skill.

Here is a video to elaborate the meaning of quickscope and drag scopes:

Uberturtles Sniper Tutorial