Okay, so the name may not be considered very PC today – you could also call this a cross-dominant stock. The concept was to allow a shooter to mount the gun in one shoulder but sight with their opposite eye. This was useful for cross-dominant shooters (ie, right handed but left eyed) or shooters who had suffered a crippling injury to one hand or one eye.
The craftsmanship involved in properly making such a gun is quite impressive. The frame and tang are made with a slight curve to them, and then the stock must be made paying careful attention to the direction of the wood grain, so that it can withstand the bending moment created when firing. A fantastic piece of work, and something generally restricted to the rather wealthy.