"You are thirsty."
Translation:Du hast Durst.
It's just the German phrasing. "Du hast Durst" and "Du hast Hunger". Durst means thirst. "Du bist Durst" would be "you are thirst". You can say "Du bist durstig/hungrig", which is a gloss of the English "You are thirsty/hungry", but no one says it like that in German. (Maybe some dialects, maybe for literary/rhetorical purposes.)
You are thirsty is different to the 'you have thirst' form because in German they like to say you have something rather than are something like in English. For example, they say, you have ill, (I believe) whilst in English we would say 'you are ill'. It doesn't really matter, but literal translations are never good.