First played by Alexander Alekhine, this provocative opening belongs to what was once called the 'hypermodern' movement in chess. Chess, until the early 1900's, had been dominated by the Classical school of thought, which strongly held that the most important aim of any chess opening was to occupy and control the center of the board. The hypermodern movement, spearheaded by Aron Nimzowitsch and his seminal book My System, overturned this and many other classical precepts, theorizing (and demonstrating in over-the-board play) that it was possible to control the center from a distance, inviting your opponent to over-extend his forces and then undermining his position.

Alekhine's defense is the most hypermodern of the current main opening lines - Black refuses to move a single pawn in response to White's 1.e4, instead bringing out his king's knight, allowing his opponent both to gain space (by pushing his king's pawn forward another square) and time (Black is forced to move his knight at least twice in the first few moves, a cardinal sin according to Classical chess theory):

1.e4 Nf6
2.e5 Nd5
3.d4 d6

At this point, proponents of the Classical mode of chess would consider that Black's position is already hopeless. However, the advanced White pawn on e5, though it seems to be a strength, cramping Black's position, can often turn out to be a weakness, requiring more and more defense from White as the game progresses. You could think of it as an infantry unit that has seized a hill too far into enemy territory. If you want to avoid losing the unit, you will have to make some major manouevers to defend it, and in the meantime your enemy can be pursuing other plans. The next moves of the main line are

4.Nf3 Bg4
5.Be2 e6

It can already be seen that black is putting indirect pressure on the White center, while completing his own development. In practice, Black's provocation can lead to a quick disaster - sometimes, if he is not careful, White will simply establish a stranglehold on the position from which Black can never recover. However, Alekhine's defense has been played at the highest levels of chess, and can lead to strange, intricate positions with a flavor unlike any other chess opening.