When something is uncharacteristic, it's not typical or expected. Snow in South Carolina is uncharacteristic, even in January.
Your uncharacteristic silence might prompt your friends to worry about you, especially if you're normally the most talkative one in the room. On the other hand, an uncharacteristic win for your school's football team may fill you with uncharacteristic school spirit. Characteristic means "typical of a person or thing," and when you add the prefix un-, "not," you get its direct opposite.