A principality is a nation, country or land ruled by a Prince.
They tend to be smaller than Kingdoms. Very little is known about the political systems of principalities. Perhaps they be a smaller region within a greater kingdom, or independent with ties to a nearby kingdom.
In present times, the continent known to some as Daventry and to others as Serenia, is broken up into many kingdoms and principalities, with two of the most significant ones being the Kingdom of Daventry, and the Sovereignty of Serenia.
There is one story of one aspiring magician who promised to rid a small principality of its overpopulation of rabbits. She entranced a fire dragon and directed it to a carrot patch that was a particular favorite of bunnies. With a theatrical wave of her wand, she directed the beast to use its breath and to, "Fire!". The dragon breathed, but due to poor eyesight, it had no effect on the rabbits who bolted back into their holes in fright, even though the flame was not cast in their direction. And so it was that the castle lost both its scarecrows, and the poor magician lost her job.