I've just been to the Royal Castle in Warsaw, Poland and I noticed that many of the portraits show the subject pointing at something, often out of the frame, for example this one.
Why is this?
The fact that the artist is unknown presents a problem in that different interpretations of hand gestures have been applied to different artists (see combination of pictorial and real space for example), especially when the subject is pointing to something out of the frame. However, there are some general 'pointers' which can be applied in many cases.
A hand with the index finger pointing but level means the person is on the path and is proceeding along it - in process as it were. There is the added implication that they know where they are going - know their Destiny.
Augustus II the Strong (d. 1733), Elector of Saxony, King of Poland, Grand Duke of Lithuania. Image source
There is a look of confidence about the portrait as a whole, that the subject knows where he is going, an image which pretty much any ruler would want to project. The gesture with the left hand emphasizes this.
Another common gesture is pointing down, representing
...their Higher spirit reaching down for the soul. The implication being that the person is not yet on the path and is being 'searched for', as they are in a state of innocence [or ignorance if you prefer].
Pointing up is also seen in some paintings, perhaps most famously in Leonardo da Vinci's The Last Supper and also Saint John the Baptist, the common interpretation being (unsurprisingly) heaven. For example,
...characters represented in paintings St. Anna and John (1498-1499?, National Gallery, London, England), Last Supper (1495-1498, Santa Maria delle Grazie, Milan, Italy), St. John the Baptist (Leonardo da Vinci, 1513, Louvre) point to the heaven. In this way, they indicate supernatural ("heavenly") dimensions of being (God, paradise, grace etc.) and "high" values.
(see also this article: St. John the Baptist - by Leonardo Da Vinci)
Generally, pointing at people or objects within the frame is used to draw attention to who or what is being pointed at.
Shearer West, Portraiture (Oxford History of Art)