The origin of this stance dates back to the first pistols and back when dueling was common. The idea was to present the least amount of body surface area to the opponent and this could be achieved by facing the opponent sideways. Another reason was that it allowed the shooter to use the other hand for something else, for example, holding the reins of his horse, or manipulating a door knob.
The one handed stance was taught in the US military for a long time, as illustrated by the image above. However, many soldiers could not manage the recoil of the Colt M1911 pistol and accuracy suffered as a result. Hence, two handed stances have been taught in recent years (which we will cover in following posts).
Many competitive pistol shooting events (such as air pistol events at the Olympic games) also mandate that the shooter should use only one hand, particularly because it is more challenging than shooting two-handed.
Notice how the shooter shoots with one hand holding the pistol and the other hand placed on the hip.