The term dual-display mode refers to the display of two independent file displays in the one Lister. Each file display can show the contents of a different folder. Dual-display mode makes it particularly easy to compare the contents of two folders, or copy or move files between two folders, without needing to open multiple windows. Another common use is to display the same folder in both displays, in two different view modes - for example, details mode in one and thumbnails in the other.
The easiest way to put a Lister into dual-display mode is with the buttons on
the default toolbar - 
for horizontal layout, and 
for vertical layout. You can also press
F6. When a Lister goes into dual-display mode,
the currently displayed folder will be duplicated in the new display. You
can change this to always show a specific initial folder in the second
display with the Specify initial folder when switching to dual file
display option on the File Displays /
Options Preferences page.
When a Lister is in dual-display mode you can copy or move files from one display to the other using drag-and-drop or copy-and-paste. Dual-display mode also ties in with the Source and Destination concept - whenever a Lister is in dual-display mode, one display is always designated the source folder and the other is the destination. This means that commands like Copy Files will always copy selected items from one display in the Lister to the other.