Magic: The Gathering is quite literally more than a game. Besides the fact that Magic is a world of its own, a topic that initiates can discuss about for hours without outsiders understanding a single word, the game does take place on three levels.
The most obvious level is that of the card game itself. Each of the two to six players takes the role of a wizard who tries to get his opponents from 20 life to zero, or defeat them in other ways. For this, he has spells, represented by his playing cards, at his disposal. Spells can be used to summon creatures that beat up the opponent or block the opponent's creatures. Other spells directly do damage, cause the opponent to discard cards, destroy creatures or do a multitude of other things, not all of which seem immediately useful.
To get more structure into the game, spells come in five colors that each have specific strengths and weaknesses. Green has fat and cheap creatures, but no practical methods of destroying other creatures. Blue has counterspells - which can prevent other spells before they happen - but is weak when it comes to creatures, and so on. It is possible to combine cards of different colors in one deck; however, this can lead to mana problems. In order to cast a spell, you need mana of the corresponding color. Mana is drawn from lands, which are again represented by playing cards. The more colors you have in your deck, the larger your risk of waiting a long time before you draw the required lands.
This brings us to the second level, the so-called meta-game. Players can build their own decks, bound only by a small number of rules: it must have at least 60 cards, there must not be more than four copies of each spell, and that's about it. Theoretically, players have thousands of differend cards from some 20 expansions at their disposal to build a decent deck. That deck should have a strategy, a good plan for defeating the opponent. Time-honored strategies include read aggro decks that overrun the opponent with cheap creatures and burn spells, or white-blue control decks that keep the enemy in check with counterspells and creature destruction until one of your creatures hits the red zone, the opponent runs out of cards, or falls asleep. Other decks rely on combos - combinations of two or more cards that, through more or less subtle interactions, achieve overwhelming effects, such as getting an arbitrarily large number of creatures into play. If you cannot assemble the combo, though, you are often helplessly watching your opponent beat you down.
However, there's a counter-strategy for every strategy: there is no deck that has no weaknesses an that cannot be beaten. Ambitious players try to anticipate what their opponents are going to play, and to devise their own decks accordingly. However, including too many defensive cards to foil the opponent's strategy dilutes the offensive strategy, and you run the risk of having many useless cards sitting in your hand. Building decks is an art and a science, and planning and testing new decks is one of the most fascinating aspects of Magic.
That takes us to the third and most unagreable level - a pure lottery. Cards are bought in small packs that cost around $3. Each pack contains 15 random cards, of which one is a rare, three are uncommon, and eleven are common. The rares are naturally the cards with the most impressive and unusual effects. That means, in order to to build an ambitious deck, you must buy and trade, buy and trade... the bottom line is, Magic can only be recommended to people with a solid income and high resistance to addictions. For those, it is a fascinating game, which for some reason appeals especially to physicists and mathematicians.