Can some British people help me here? (Or people who know about this)

Why is prince William the 'Duke of Cambridge' and Prince Harry the duke of Wales and Charles of Wales as well? 
I dont get it why their children get like a city or area ?
Dont judge please I'm American and thats interesting, sadly our teachers dont tell us about international stuff like that...
Oh and is their last name Windsor ? Because on Wikipedia it only says Prince William, Duke of Cambridge and his titles are followinf.