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Counting cards in blackjack is a method of calculating whether the undealt portion of the deck is rich in high cards, or weighted down with low cards. High cards are good for the blackjack player. Low cards are good for the dealer.
Consider the implications. If the dealer's hand totals 16, the dealer must hit. A deck rich in tens increases the odds of the dealer breaking (going over 21). A deck weighted down with lots of low cards increases the odds of the dealer ending up with 20 or 21, bad news for the player. Also, a deck full of low cards decreases your chance of getting a blackjack.
Card counting assigns a number to every card denomination, and the number can be a plus or minus. When the deck is shuffled the count starts anew at zero. As the cards are exposed, you would add or subtract the number assigned to that denomination from the count. This updated number is called the Running Count.
For example, the Hi-Opt I counting system assigns the following numbers to each card:
Card

Simply put, ten value cards are counted as -1 (minus 1). Threes thru sixes are counted as +1 (plus one). The rest of the cards are ignored. The following table shows the Running Count thru two hands of blackjack play.
Card Dealt
Count
Running Count
First Hand

Do you see what happened in the second hand? Many tens were dealt, hence the Running Count was a negative number. Had most of the cards dealt been between 3 and 6, the Running Count would have been positive. The negative Running Count would reflect a deck rich in low cards, as many of the high cards have been dealt. A positive Running Count would signify that a lot of low cards had been dealt already, so the deck should have a higher proportion of high cards left.
There are many different counting systems, and not all systems start at zero with a newly shuffled deck. Some systems are Balanced Systems, meaning that if you take one complete deck of cards and count it all the way thru, your final Running Count will be zero. An Unbalanced Counting System does not end up at zero after counting thru the deck.
The Running Count is used to determine whether to hit, stand, double, or surrender, as well as how much to bet. A player may bet much higher if the deck is rich in high cards, which increases his likelihood of being dealt a blackjack. It is extremely important that you understand that Card Counting is designed to work with Basic Strategy. If you do not religiously follow Basic Strategy, you should not attempt to make decisions based on Card Counting.
When multiple decks are used, which is most common, the Running Count should be adjusted to reflect what is known as the True Count. This adjusts the Running Count by the number of decks left. Another very important factor in Card Counting is how much of the deck is dealt before the dealer shuffles. This is called Penetration. If the dealer deals out 75% of the cards before shuffling, this is considered 75% penetration. Higher penetration means more cards are dealt before shuffling, and your count will more accurately reflect what to expect. A penetration of 70% or less should be avoided.