DragAndDrop is an option for Cell which specifies whether to allow drag-and-drop editing on the contents of the cell.
With DragAndDrop->True, dragging an already-selected region cuts the region from its original location, and pastes it at the location you move to.
DragAndDrop is more often set as a global option in the front end, rather than as an option for individual cells.
See The Mathematica Book: Section 2.10.11.
See also: StructuredSelection.