When something is shivery, it gives you the chills or makes you feel cold and shuddery, like a spooky ghost story told around a campfire on a dark night.
Shivery comes from the Middle English word chivere, which some etymologists believe is an alteration of chavele, which means "to chatter." The reason for this belief is because the word is thought to be mimicking the sound of trembling or chattering teeth. To remember its meaning, just think of the sensation you get when you're cold or scared — it's like a trembling feeling running down your spine.