When you are playing a card game, card advantage always comes into play. This isn't so much when you're playing Hecatomb where you're drawing two cards a turn, but it might be different when it comes to ordinary ones where you play with one draw per turn. Since I'm most familiar with Magic, so I'll be talking about card advantage in Magic. (I'll be using a number of pictures, most of which I have taken from Magiccards.info, but the copyrights belong to Wizards of the Coast or Hasbro, I think. I thank Imageshack for their bandwidth. :D)
In Magic, the idea is to win. The main reasons why card prices can escalate is because of card quality. Card advantage is difficult to gain in Magic since card avdantage can literally crack the game. This leads us to the easier way of winning a game: play better spells than your opponent. You win a Magic game by having card quality advantage of sheer card advantage over your opponent. Your 4 mana to cast 4/4 creature will obviously stomp all over his army of 1/1s. He would be spending tons of cards to stop your 4/4. The quality of your single card beats the quality of his by several times. This leads to card advantage in the long run. Card quality is important, but sometimes card advantage can win the day. If your opponent had 4 1/1s, you would think twice before attacking with your 4/4. If your opponent had 20 1/1s, he has practically won the game already.
In Magic, card advantage is difficult to gain. There are some obvious examples, such as the following:
If you hit five mana on turn 6, they do the exact same thing at slightly different costs (if you played Arena on turn 3). Phyrexian Arena is obviously better for most people - it's a long-term investment that'll serve you up till you run out of life. Tidings is also good. It'll give you card advantage nearly immediately and it doesn't need you to wait for for you to recoup your investment. 5 mana for 3 cards (4 cards minus 1 which is the Tidings) worth of advantage.
Why is card advantage important? Card advantage gives you power. It's a simple way to reason. The more cards you have, the more power you have. You can play more lands than your opponent ever could. You could play more creatures than your opponent could handle. Your sheer card advantage can trump his card quality advantage. So what if your opponent has a 4/4 on each turn if you could come up with more and more 1/1s to stop him with.
Card advantage gives you the ability to control the game. If you could trade every single card with your opponent on a one-for-one basis into the graveyard, the one that draws more cards will be the winner. There is no need to skimp on blocking his creatures with your own, or destroying that creature with the single cards that you have since you're going to win the race anyway.
Then, I show you one of the cards that define card advantage:
One card that can destroy any other creature on the board. Depending on how many creatures your opponent has, this one card can produce more card advantage than any card drawing can get you. You want proof? Here's one that generates so much card advantage you have to give up all the cards you're holding in your hand. :D