I think this is to mount 1 or two extra flash units on a light stand or tripod. Back in the days of bulb flashes, there are unpowered units called "extension flashes". You use an extension cord from your main unit to the extension flash. The extension flash is mounted off camera, to illuminate the background, or to act as a main light, hair light, etc.
The extension flashes that I own have 1/4" x 20 tpi sockets in the bottom. However, it's easy enough to buy tripod screw to cold shoe adapters, screw these onto the bottom of the flash, and slide the flash shoe into the cold shoe of this unit.
With the device that you have, you can also use electronic flash in the cold shoes, AS LONG AS THE FLASH UNIT DOES NOT HAVE A HOT SHOE! If it has a hot shoe, the metal of the cold shoe will create an ongoing short circuit. This also applies to bulb flash units such as the Nikon BC-7, which incorporates a hot shoe.