By offering a narrative example of the dangers of certain social and political attitudes, plays like The Crucible provide a relatable and somewhat concrete model of these dangers. This can go a long way to highlighting the overlooked and un-reported sides of a political story, social attitude, etc.
We see the danger clearly when it has been humanized and put into story form, dramatized for effect and simplified down to its most significant elements.
The way stories/plays like this are able to address social issues so effectively is that they display the problems in a way that an audience is able to read/view the tragedies and problems of others from a distance and still apply the principles to their own lives. For example, the lies told by Abigail and others remind us that lying can lead to devastating consequences. Being greedy is a bad thing, as is adultery; and we can see the results in other people's lives and apply that to our own in the hopes of preventing our own personal disasters. We still do those things, of course, but at least we have been warned.
In general, tragedies like this show us the sort of impulses that drive people. Often, these impulses are connected to social issues. For example, in The Crucible a major reason that some people get accused is the fact that others want wealth and/or power. When this happens in a tragedy, it reflects the importance that people in our society place on such things. In that way, it reflects a social issue (greed, excessive desire for power) that is important in our society.
One of the way that Miller's work reflects social issues lies in its construction of power. Miller creates a setting in Salem where moral absolutes are brought into severe questions because of contingency. Miller is vociferous in his contention that the modern setting requires an examination of context before any absolutes can be offered. For example, the supposedly morally infallible idea of telling the truth is something that has to be examined in its proper context. If the government or the ruling body is corrupt, or seeks to manipulate truth for its own benefit and to its own ends, there is a reexamination of the moral absolute. Politics is a domain where individuals have to be mindful of agendas being advanced and how institutional checks can limit any manipulation of government. Miller's drama reflects this particular social element because it seeks to bring out the idea that governments can be corrupt and individuals have to be mindful of this before believing in ruling bodies' claims of authenticity and purity.