Card counting is an advanced technique than can be used when playing games like Black jack. Counting cards when playing Black Jack is about keeping track of the relation between high and low cards in deck that is being used. The more high cards left, the better are the odds of winning. If one masters this technique can one get an advance towards the house.
The American mathematician Dr. Edward O. Thorp is known as the father of card counting. In 1862, he published the book "Beat the Dealer" where he discusses several strategies and techniques used when counting cards in a game of Black Jack. Even though new techniques have been developed since and the fact that casinos around the world have taken great measures (for example by never dealing until the last card in the deck) "Beat the dealer" is still considered a great and valuable hand book for card counting.
Although Thorp was the first one writing a book on the topic there were others before him. Jess Marcum was a member of a group of professional card counters that was beating casinos in Las Vegas and other places. This was in the 1950's and Marcum is regarded to be the one who developed the first point value system to count cards.
A common method to count card is the Hi-Lo method which is single-level or level-one counting because the counting never increases or decreases by more than one. Every card in the deck is assigned a point-value (2-6 value 1, 7-9 value 0, 10-Ace value -1). The values are then added and your decisions are then based upon the total value of the number of cards still in the deck. There are of course even more advanced systems and ways to count cards.
In order to make counting cards work at all it requires that the house doesn't shuffle the deck too often, that it doesn't use too many decks and also they can't be using rules that are disadvantageous to the player. Examples of unfavorable situations for players are to be seen on Swedish Casino Cosmopol where they shuffle the deck after every play. By doing so they eliminate every chance to count cards. Another example of unfavoristic against the players you can find at restaurants and pubs where they offer Black Jack. Their rules are very disadvantageous and they also have a betting limit to further protect themselves.