Alekhine's earliest tournament games with the defense were at Budapest, 1921 against Fritz Saemisch and Endre Steiner but it was simply called "Irregular."
Chess historian Edward Winter writes that when annotating one of the games in BCM, Sir George Thomas wrote that this "novel" defense was introduced by Alekhine there and since then it had been subjected to further testing by other players. Thomas went on to say that it was tentatively named Alekhine’s Defense, adding that it was a "novelty of considerable importance and it opened up a new field for investigation." Winter also tells us that in 1922 in the first monograph on the opening, Die Aljechin-Verteidigung by Hans Fahrni, he called the opening "Alekhine’s Defense."
It's popularity waxes and wanes but Vassily Ivanchuk and Lev Alburt championed the defense and made many contributions to its theory and practice. Shabalov and Minasian occasionally use it as do Aronian, Adams, and Nakamura. Fischer and Korchnoi also had it in their repertoire.
The strategy of Alekhine's Defense is to tempt the white Ps forward with the hope of then undermining white's expanded center. White has to prove that the extra space is advantageous and often uses his space advantage to attack the black K. For his part, black tries to use tactical means based on the weak squares and Ps that White has created.
White has several strategies: the Four Pawns Attack, the Exchange Variation, Modern Variation, Balogh Variation, Two Pawns Attack, Two Knights Variation as well as several sidelines. These days you'll mostly see white playing the Modern Variation (1. e4 Nf6 2. e5 Nd5 3. d4 d6 4. Nf3) which was made popular in the 1972 Spassky-Fischer match.
Today's game features The Four Pawns Attack which is white's most ambitious try, and the variation which perhaps illustrates the basic idea of the defense best: black allows white to make several tempo-gaining attacks on his N and set up an imposing P-center. White then must find a way to use his advantage in space before black succeeds in attacking and destroying it.