Movies are cut most often due to time on screen.
Hard work for folk to sit for more than two and a half hours of anything.
Then there's the role the censors play.
Censors can insist on certain shots; frames; scenes being re-shot or removed completely if it has consensus that they are too graphic (sex; violence; drugs; abuse etc.)
This is important because it depends on the rating given to the movie as a result.
eg: It's harder to rent movie theatre screens for an R rated movie than it is for an 18 certificate for example.
Why ? Because the likes of the big studios that own a larger slice of the movie theatres can decide whether or not to show a movie based on it's classification alone !
The Director Ron Howard once said
The first thing they teach you at movie school is Be prepared to cut your favourite scene
. For all the reasons listed above.
So i guess some Director's cuts are the film with the scenes that had to be cut for cinematic release.
There's a brilliant documentary called "This film is not yet rated" by Kirby Dick and Eddie Schmidt (2006) that explains how it works and feature comments from well known Directors and Producers on the subject
