Duchy is an area ruled by a man who held the position as a duke. In countries with monarchy system, duke is one of the highest rank in the Kingdom, Bested only by the members of the royal family (Kings, princes, queen, etc)
Kings usually gifted their dukes with a territory. The duke has the power to control all the government process within this territory. So technically, it can be considered as an independent nation. But the duke's power only limited to their borders. As long as he stepped out , other dukes will take over the power. the King also can override this power whenever He pleases.
