The Unit Publicist organises cast interviews and visits to the set by journalists while the film is shooting. You know all those bits on Entertainment Tonight where they are on the set visiting with the stars during filming? Well, the Unit Publicist set that up. They also get mention of the film into the trades as well as local papers (especially if the film is not being shot in Hollywood). It’s not always an easy job as the stars are usually doing this on their own time and are not always cooperative.
They also write press kit information (biographies, story synopses, etc.), maintain photo files (write IDs, get artist approvals) and assist the stills photographer with posed shots. To get into this line of work: journalism or public relations education/experience and some experience with photo editing are appropriate background (and a degree in advanced psychology would be useful!)