A blocking card is a card held by a player that makes draws and redraws by opponents impossible.
For example, in hold'em, the board on the river is
You have a straight flush and there's no possible better straight flush because you hold the 9 of hearts, which blocks any better straight flush.
It's rare to discuss blocking cards in two-hole-card games like Hold 'em because it's rare that a player's single card could possibly block another player's better hand: the only two examples are cards which block straight flushes (as above) and cards which block quads, as in the following example. The board on the turn is:
You have quad fours. There is no possible hand that can beat you right now, but in theory, the river could bring another eight, and another player could have pocket eights which would make them quad eights and beat you... except you hold the eight of hearts, which makes that impossible (even if another player held pocket eights, that would mean there were no eights left to come on the river). So, if another eight does fall on the river, you are assured that no player can possibly have quad eights, because you hold the blocking card of the eight of hearts.
In games where players have hands of more than two cards, blocking cards are much more common, because players hold many more cards which could block other players' hands (and, in some variants, because many more cards are generally known to all). For example, in a game of seven-card stud, if you have a pair of queens as your downcards, you are certain that another player cannot have trip queens, even if they have a pair of queens in their upcards. Other players at the table may not be certain of this, and the player with the pair of queens showing may bluff as though he had three of a kind - but you hold blocking cards to ensure that it is impossible for him to have such a hand.