One of the reasons this play is so famous is that Miller wrote it at a time of mass hysteria, and thus used another historical incidence of mass hysteria to comment critically upon McCarthyism and the savage way that it targetted innocent individuals. Let us focus on the parallels that exist between the Salem Witch Trials and the mass hysteria and paranoia concerning communism that occurred in America in the 1950s.
Both eras of course present those who are responsible for eradiating either witchcraft or communism as being over-zealous, narrow-minded and ignorant. In addition, those accused of being Communist were encouraged to name others who were Communist, just as the "witches" were supposed to name others to save themselves. Lastly, let us remember that McCarthyism found many innocents to be guilty, just as innocents were hung as part of the witch trials.
Miller wrote this amazing play therefore to cast a very critical gaze on his own times and what was going on. Interestingly, juxtaposing McCarthyism with another historical period that is so distant and yet so similar in so many ways shows that humanity has learnt little over the intervening period.