So I hear you ask; 'what is a directors cut?'

A directors cut is defined by google as 'a specially edited version of a film, and less often TV series, music video, commercials, comic book or video games, that is supposed to represent the director's own approved edit.
It is considered that a directors cut is aimed to show the thoughts and feelings the director was feeling, whilst producing his media product. Whether it be why he used certain shot types, costumes, lighting, etc.
A directors cut, also known as a directors edit, will often be found on a seperate disk. They show the media product, with the directors dialogue played over the top of the video shown. Often only true fans watch these as they are most interested in the thoughts and opinions of the director.