Translation:It is something you can be proud of.
The "dont" is a relative pronoun replacing de + person/thing/idea and it joins two thoughts. C'est une chose. Tu peux être fière de cette chose. = C'est une chose dont tu peux être fière. Said another way this sentence could read, It is something (of which) you can be proud.
The English "of" in this sentence does arrive as a translation of the French "dont", but more generally, in this type of statement in English, the preposition paired with "proud" is "of".
Someone or something can just be "proud" in English: "He is proud". But if the verb "to be proud" has an object it is connected to the sentence with the preposition "of".
So you get sentences like "I am proud of you." Or "He is proud of his pet goldfish", as well as the sentence in this exercise: "It is something you can be proud of." Some people avoid ending sentences with prepositions, so you could say "It is something of which you can be proud". Either way works.
According to "https://www.youtube.com/watch?v=uauZvVrWGhY", the masculine "fier" and the feminine "fière" are pronounced identically, which is what I always thought. (The voice synthesizer mispronounces the masculine "fier".) So either "fier" or "fière" are correct in the dictation exercise.