A duchy is the jurisdiction of a Duke. You'd have to check out the specific duchy for more detailed information. A good place to start is the British Royalty website.
It was the Kingdom of Bohemia, a country that occupied pretty much the western half of the current Czech Republic. During the Hundred Years' War, a Bohemian king called John I fought and was killed...
A Grand Duchy is a state ("nation" in common, modern language) in which the Head of State (the ruler) is a Grand Duke.
Similarly, a Duchy is a state where the ruler is a Duke