A whole lot of fancy, analytical text could go here, but the best summary one can give of A Clockwork Orange is that if you talk about it to a guy in his 40's or 50's and his eyes start to light up, FUCKING RUN.
The movie focuses on 17-year-old Alex, the scary-looking guy up top there. Alex and his buddies spend the first half of the movie drinking drug-laced milk, and then going out to enjoy "a bit of the old ultra-violence". This includes stomping on a homeless guy, fighting a rival gang that was in the middle of raping a woman, stealing a car, and driving out to a country estate to beat the resident...and then rape his wife.
All in a night's entertainment.
Soon, though, his gang tires of his tyrannical leadership, and betrays him at just the wrong time, sending him to prison. To get out, he volunteers to go for a radical treatment, which leaves him feeling physically sick whenever he contemplates violence or rape. This leads to the second half of the movie, which would give anyone who believes in the concept of karma a raging hard-on.
But...shouldn't they find this more appealing?
Long story short, every single person that he wronged in the first half, gets some form of retribution in the second, usually consisting of beating the crap out of a guy who can't fight back or else he vomits uncontrollably. It culminates with him stumbling to the home of the who he assaulted and whose wife he raped. He locks Alex in the attic, and drives him so insane with music that he decides to leap out of the window and try to kill himself. He recovers to the head of the government apologizing for the treatment, and saying that it had been removed, leaving Alex free to rape and kill again, thereby confusing the audience about whether they should laugh or cower in fear.
All's well that ends well!
It wasn't favorable, at first, with Ebert calling it "an ideological mess". Still, over the years, it has amassed a cult following, making them one of the cults that you probably don't want to run into, yet would be full of middle aged, normal looking men.
Here's a tip: If they're discussing the artistry of this scene, just walk away.