I agree with Abdul's explanation, but translating it literally wouldn't reflect the meaning. The release of the director's cut later on is attractive to the viewers for the mere reason that they get to see all the scenes they missed on for a variety of reasons, e.g. to decrease the duration of the movie, decrease the rating regarding violence & sex, etc... So basically it is the longer version of the movie.

Simply, the version as intended by the director -- when several versions of the movie exist, e.g. TV Version, Theater Release, etc., one of these version represents the movie's first final-cut made by the director.

Although I am sharing references with Samir, I am more concerned about the following paragraph:

Wikipedia:
"With most studio films the director does not have final cut. The studio can insist on changes to make the film more likely to succeed at the box office. This sometimes means happier endings or less ambiguity. Most common, however, is that studios ask that the film be shortened. The most common form of director's cut is thus to have extra scenes added making films often considerably longer."

Director's Cut versions are sometimes referred to as Unedited Version or even Uncensored Version, depending particularly on each instance.

An example of that is Resident Evil, the Playstation game, where the original openning sequence was replaced in the American and European (NTSC, PAL) versions of the game with a less-gore black and white version. The game was re-released later with the unedited Japanese openning in Europe under the title Resident Evil: Director's Cut -- the game in itself was modified, but the name was used for the Openning Change incident. The American version witnessed no change in the openning movie, which Capcom apologized for with a downloadable unedited version on their website.

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Note added at 1 hr (2006-08-14 13:03:32 GMT)
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typos:
these versions represent
opening - sorry about this one; japanese influence ^^;