Anthony Burgess, the author of the novel, distanced himself from Kubrick's adaptation for "glorify[ing] sex and violence."
The glorification part is up for debate, but one thing is for sure: the film is chock-full of sex, violence, and sexual violence. The film was rated X when it was originally released in the United States. The modern equivalent of this rating is NC-17: no children, cats, dogs, or squirrels under seventeen years of age admitted.
The X-rating was mainly given to pornographic films, although A Clockwork Orange and Midnight Cowboy received this rating and still got Academy Award nominations, so it wasn't entirely for smut.
When released on VHS, the film was censored for an R-rating. However, the X-rated cut was eventually re-rated R and re-released on DVD. So unless you're dusting off an old VHS from your grandpa's attic, you've actually seen the original X-rated cut.
Strangely, cinema seems to have regressed in modern times. Films as explicit as A Clockwork Orange are rarely seen today. Even Kubrick's Eyes Wide Shut was censored in 1999 to avoid an NC-17 rating, and an uncensored cut has never officially been released in the United States (source).