There are many resources in Magic, but the most basic and universal of those resources are cards, which obviously every deck contains. Card advantage is a word for a deck or player getting the best use from those resources.
Defining card advantage
In basic terms, each card that is drawn allows the player to get closer to however it intends to win the game, and the same is true for the opponent. Gaining card advantage over your opponent means that you are closer to having the right cards to win the game than he is. Card advantage is an incremental advantage and is mainly associated with control decks, who seek to gain advantage over time before delivering a killing blow, while it is not particularly relevant to aggressive decks that seek to win quickly at the cost of card disadvantage while their opponent is still drawing cards and finding the right pieces.
In a normal game, each player has 60 cards with which to win the game, but they in fact have access to far fewer cards than that, because of the restriction on hand size, and only drawing one card per turn. So, on its most basic level, drawing more cards than your opponent generates card advantage, because doing so gives you access to more resources than he does.
Efficiency
However, simply drawing more cards is not the only factor in card advantage, and it similarly applies to how efficiently cards are used. If everything were equal, then each card played would be cancelled out by the next card played by their opponent. If this were the case, neither player would have any card advantage. However, if the second player can instead use one card to counteract two of his opponents, then he has gained card advantage which leaves him with more cards in hand (ie with more resources available). This can be achieved either through using inherently more powerful cards (using one Wrath Of God to kill two creatures instead of two Incinerate) or through playing in such a way as to create a 'two for one' situation even with a weaker card. An example of this would be using Incinerate to kill a creature in response to your opponent casting Giant Growth on it. This kills his creature and means his Giant Growth has been wasted, leaving him with one fewer resource to use. A third way to gain card advantage is to use a spell which cantrips while also achieving the desired result. For example, if a player responded to his opponents Giant Growth by casting Repulse on the targeted creature. The growth would still be wasted, at the cost of one spell cast. The creature returns to its controllers hand, rather than killing it, would mean that this is an equal trade. But as the first player also draws a card, he has gained an extra card over his opponent, thus achieving a two for one, but in a different way. Finally, a player can simply draw cards through spells or abilities. Some spells like Divination simply draw lots of cards while others like Ponder allow the player to chose which card they draw.
Pitfalls
Each of these has their disadvantages from a gameplay stand point. More powerful cards like Wrath cost more mana, which is not always available, only able to cast past a certain point in the game, which can be too late for some decks. Waiting to use a removal spell until you get an opportunity for a two for one can mean you wait forever, taking damage all the while. Finally there are few cantrips available and in fact there may not be such a spell, and even if there is, they will always cost more than a single spell alone. Just drawing cards, while a powerful effect in terms of providing your deck with the resources it wants to have, simply drawing cards alone will not win the game, nor in fact interact with the opponent alone. Sometimes, most often early in the game, choices have to be made that are more concerned with protecting life total than creating card advantage. This is often fine, because an aggressive player against whom such a choice is likely to need to be made, is unlikely to be able generate card advantage himself and thus once you have weathered the storm of his initial attacks, you can decisively gain the card advantage once your more powerful spells are available.
Mastering the concept
As is hopefully clear by this point, card advantage is a difficult topic to describe. However, learning the concept of what it is, and how to gain it allows you to win games that might otherwise be impossible. However there will often be a choice between simply protecting your current position, and gaining card advantage, and knowing which to pursue is one of the most challenging aspects of magic, and mastering it will make you a far better magic player. If an opponent is forced to use a card to protect his creature or spell (perhaps using Vines Of Vastwood to save his creature) then you remain equal in terms of card advantage (you lose one card, as does he) but he maintains an advantage on the battlefield. In this situation however, other things are also happening in terms of incremental advantage. If, for example he was not able to cast Vines with kicker, and therefore had to use it exclusively to defend his creature, then you likely do gain some advantage, because you force him to use a card that he would rather use in another much more aggressive way. If you are very low on life and have to use another removal spell to survive, you lose care advantage, but you gain another turn to draw cards and find a more permanent solution.
Card advantage is often the defining factor in control vs control matches, with the victory not going to whoever topdecked their finisher, but who best optimized their use of mana and cards, so that they had the mana to cast their win condition, and created the most opportunities to make that draw.
On the other side to card advantage from drawing cards, you can attack your opponents hands to create advantage by using spells that make them discard. Untargeted discard is the least desirable, as it allows them to pick which card they can manage best without, while targeted discard such as Inquisition of Kozilek can allow you the opportunity to attack either the opponents creatures to protect the board, or their own card advantage engines, depending on the game state.
A final approach to gaining card advantage is through cards which can be used multiple times, through mechanics like Buyback on Forbid, or using cards that fill multiple roles in your deck like Snapcaster Mage, Venser, Shaper Savant or Mystic Snake
Tempo
Tempo is another concept closely related to card advantage, which seeks to win not by directly killing his creatures, but by disrupting his mana curve by bouncing creatures and drawing cards. In these types of deck cards like Remand when used correctly can be a Time Walk giving you access to more mana (both by being cheaper than any other catch all hard counter, and giving you another turn to play a land), buying time, and protecting your board position and replacing itself in your hand. While on the surface Remand is a one for one in terms of card advantage, you gain 'half a card' in that situation, because while your opponent remains with the same cards as he had last turn, you gain another card from your library.
Color Pie
Blue is the colour that is most associated with card advantage as a mechanism to win games. It contains the most cantrips, as well as the most pure card draw and deck manipulation. It is certainly possible a purely blue mage to stall out a game long enough, using continuous counter magic[1] , bounce spells and end of turn card draw (or cards that allow all of the above like Cryptic Command) until they get a bomb Consecrated Sphinx (which doubles as a card drawing engine) to fly in the damage they need. However, these approaches while very good at gaining card advantage are seldom the best ways to win games or protect the board state. Black provides discard and mana-efficient kill spells to disrupt the opponents game until your counter magic gets into gear. Red offers aggressive creatures to block in the early game or apply pressure, and reach in the form of Fireballs to close a game out from nowhere. White gives some of the best spells to gain card advantage through destroying creatures in Wrath effects (which can turn into a 5 or 6 for 1), as well as a string of little dudes either with interesting effects (first strike, flying, protection) or as cheap and efficient token makers along side Glorious Anthem effects to block or eventually to gang up and charge into the Red Zone. Finally Green offers mana acceleration to quickly move your deck from the troublesome early turns, where card advantage is much less relevant and harder to find, right up to six mana, allowing for multiple counters or draw spells in a turn, pushing card advantage from incremental to decisive, and of course offering casting a massive green creature of stompy goodness, while leaving enough mana to counter anything that threatening it.
Conclusion
Card advantage comes from many different places, but in some respects almost every decision you make in a game of magic is made with it in mind, subconsciously or not. Learn how to gain incremental advantage and it adds up faster than you might think. Again, this article is not perfect, because no-one really agrees on exactly what it consists of. But hopefully this will give you a better understanding of what it is, how it works and why it is so very important.
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