A card that when it appears makes a better hand more likely. In hold'em, a third suited card on the river is a scare card, because it makes a flush possible. If you're pretty sure your opponent paired a king on the flop, an ace on the turn is a scare card. Scare cards will often make it difficult for the best hand to bet, and offer an opportunity for bluffing. Obviously such cards are scarier in pot-limit or no-limit games.
a card that stands a good chance of destroying what would have otherwise been a leading hand. eg: you've got Td8s, the flop was Js9h7h and you've almost certainly got the leading hand. A Qh on the turn would be a scare card because it means that your hand is quite possibly ruined. A higher Straight or a Flush are both probable and both would beat you.
A card which is dealt face up which makes you not feel as confident in your hand. Ex. You hold a pair of Kings in Hold'em and an Ace shows up on the River.