The difference between bad and horrible is like the difference between an unpleasant dream and an awful nightmare.
Horrible means "causing horror," and goes back to the Latin word for “tremble” or “shudder.” A horrible thing makes you shake with fear, like a story about an atrocious crime. We also use horrible hyperbolically (which means in an over-the-top way) to criticize things. You might think you look horrible in photos, or that a new TV reality show is horrible. Do you ever wonder if something horrible is hiding in your closet? I mean, besides your plaid suit?