This question is relatively subjective, but I can tell you what my perceptions are.
When Arthur Miller wrote The Crucible, he was making a political statement. So while the story takes place in late 17th Century Salem, Massachusetts, it is addressing a situation also taking place in America in the 1950s, the age of McCarthyism.
While the 1950s may seem as distant to you as Salem during the witch trials, what you might find interesting is why "witch hunt" became such a common phrase during Arthur Miller's day. In Salem, people were making wild and unfounded accusations against members of the community, accusing them of dabbling in witchcraft. Abigail wanted John Proctor so she did all she could to get rid of his wife, Elizabeth: this sounds like something you might see on the news today or on television.
You drank blood, Abby! You didn't tell him that! [...] You did, you did! You drank a charm to Kill John Proctor's wife. You drank a charm to kill Goody Proctor!
This is only the first step Abigail takes against Elizabeth. Later Goody Proctor is accused of being a witch. The only reason she is not hanged is because she is pregnant.
Other people accused landowners because once someone was tried and executed for practicing witchcraft, his property could be bought by anyone. So men that argued over land or boundaries or wanted to get more land would accuse another or find themselves accused.
It is hard to deal with this kind of maniacal behavior. Imagine being accused of something you did not do, without any solid proof to condemn you. In honesty, I find this aspect of the play difficult to take. Salem was a place where madness reigned—UNTIL the governor's wife was accused! That put a stop to the chaos, but not until nineteen people lost their lives.
Fast forward to the 1950s: Senator Joseph McCarthy had his own reign of terror during the Cold War when everyone was afraid of being spied upon or attacked by the Russians. McCarthy started his own witch hunt by accusing people of being communist—not necessarily based upon facts, but upon suspicion, dislike or disagreement. McCarthy was especially hard on those who would not conform to his ideas: many of these people were artists of some kind—painters, writers, actors, etc. Many lost work, and their reputations were ruined for good, even after the age of McCarthyism was ended.
The following quote is about what happened in Salem, but it is also exactly what occurred during McCarthy's insidious and insane power play in Washington:
Those accused of witchcraft were hounded by representatives of their community (and the larger pressure of majority opinion) until they admitted their involvement, naming others involved in suspicious practices—although the majority of those accused and named were guilty of nothing more than behavior that did not conform to the societal norms of the time.
Here again is that desire for people to conform. While some people questioned were careful to back down and remain silent, others refused, drawing McCarthy's wrath down upon them.
In the early 1950s, hearings at Senator Joseph McCarthy's House Un-American Activities Committee had decided that the American Communist Party, a legal political party, was compromising the security of the nation by encouraging connections with Russia.
Those with communist affiliations were questioned, free speech curtailed and reputations destroyed. Those accused were encouraged to name others who were communists, non-conformists or just generally outspoken. These accusations were not based on facts, but many times actions of desperation by those accused. Those on the committee...
...often branded witnesses as "red" if they refused to comply or hesitated in answering committee questions.
To implicate others was to "redbait:"
...to denounce or deprecate as a political radical, especially to accuse of being communist.
Imagine if a band, athlete or actor you really liked or admired was accused of something that was unfounded, but prevented that group or person from performing, playing, making CDs, getting parts in major films, supporting himself and his family, and generally being ostracized simply by someone's suggestion.
In both situations, fear prevailed for quite some time. No one could ever be certain if he or she might be accused next. The difference was that in Salem, lives were lost, while in America in the 1950s people lost their jobs, reputations and livelihood without any offense other than having an unpopular political affiliation, or being suspected of being sympathetic to that political party.
Another reason the play may not appeal to the modern audience is that the behavior of Salem's puritanical society was so oppressive. The Puritans were so strict that laughing too loud could be punished. There were no parties (not even for birthdays) and the ministers preached fear of eternal damnation to the church's members. The Puritans wanted to exercise complete control over the community's members. There was no separation of church and state: the church governed every aspect of a person's life within the community. However, they ignored the entire basis of the New Testament with regard to loving and forgiving each other. (This behavior is relevant even today.) Ironically, such staunch promoters of the "fire and brimstone" doctrine were greedy, hateful and lying individuals. As with any religion, there were those who knew how to go to church, but refused to recognize that loving behavior and actions above reproach are what make a person decent or "holy."
It is hard to read about people being mistreated without any recourse. Leaving the community was not as simple as it would be today. For being out on one's own in the wilderness that stood beyond the boundaries of the town—especially when the cold weather came—would most likely result in death.
The language may also make the play uninteresting to the modern audience. Instead of "Mrs.," they used "Goody." Contractions are not used. Some of the wording may well be unfamiliar to the modern audience. The syntax or word order is also much different than the way we speak and write today. For example, this is how Abigail speaks to Danforth when he questions her integrity with regard to her testimony and actions:
I have been hurt, Mr. Danforth; I have seen my blood runnin' out! I have been near to murdered every day because I done my duty pointing out the Devil's people—and this is my reward? To be mistrusted, denied, questioned like a— [...] Let you beware, Mr. Danforth. Think you to be so mighty that the power of Hell may not turn your wits? Beware of it!
If you can get past the way that Abigail speaks here, you will understand not only that she lists the ways she has suffered in being godly (which is a horrible lie), but that she also threatens Danforth. He is the judge at these proceedings, and not afraid to hang anyone. What kind of power Abigail must know she has by threatening the most powerful man in all of these proceedings.
The last thing to consider is whether the play is being read aloud in class or if you are reading it on your own (which was not what the author intended). Reading a play alone is a truly difficult task. At the same time, if it is read aloud and no one puts energy or emphasis into the reading (which students are often hesitant to do), it is like reading the dictionary.
Do your best to follow the plot development; but then I would also suggest that you read the eNotes summary of the play (The Crucible) and character descriptions. This may actually make it easier to follow the action of the play and be of help in understanding discussion and prepare you for any test you might need to take.