What does the saying your hair stood on end mean?

In popular usage, it is comparing a person's reaction to a shocking event to that of a cat or dog.

Your hair (except for scalp hair) will "stand on end" but since most of the hair on a human is not as obvious as a cat's or dog's, you will most likely describe the change of the texture of the skin...you get goosebumps.

A hair is equipped with a muscle called the "erector pilus". When it contracts, the hair stands up, away from the skin. It makes cats look larger and serves as a non-verbal cue to other animals that trouble is about to happen. It also traps more air in the coat of an animal to provide more insulation when it is cold. Our hair still does it even though it serves no useful purpose.

When a dog's hair "stands on end" because of some sort of stress or threat, it is interesting to note that it is called "getting its hackles up". Hackles are the neck feathers of a bird. Birds raise their hackles to threaten, warn and court. You can also "get your hackles up" when you get angry even if you don't have feathers.