"My horse is brown."
Translation:Το άλογο μου είναι καφέ.
The second accent is used to make the pronunciation of the sentence smoother. When, as in this case, there is a word that is accented on one of the first syllables and a short unaccented word follows we add an accent to the long word to make it sound better. So that "άλογό μου" sounds almost like one word.
If you didn't have both accents Duo will say you have a typo but your sentence will be accepted as correct.