A shudder is an involuntary vibration, usually in your body, or the shaking itself. A cold breeze or an unpleasant memory might make you shudder.
A shudder isn't always a bad thing. It can mean a pleasurable sensation or tingle that goes through your body, like a shudder of excitement you feel when you see your favorite star on the street. As a verb, shudder means to shake and shiver. Being really cold or seeing something that scares you — a ghost! — can make you shudder. The phrase "shudder to think" means just the thought of something upsets you enough to shudder.