DragAndDrop is an option for cells that determines whether to allow drag-and-drop editing on the contents of a cell.
With DragAndDrop True, dragging an already-selected region cuts the region from its original location, and pastes it at the new location of the cursor.
DragAndDrop is typically set as a global option in the front end, rather than as an option for individual cells.
See The Mathematica Book: Section 2.11.11.
See also: StructuredSelection.