To horrify is to cause someone to feel shocked and disturbed. It may horrify your parents if you announce that you're dropping out of school to become a professional clown.
Things that horrify you fill you with terror, shock, or disgust. It would horrify you to run into a vampire on a dark city streets, and it would also horrify you to be served raw hamburger for lunch. The emotion that arises when something horrifies you is horror, a word that's the same in Latin, with the literal meaning "a shaking, a trembling, or a shudder."