Holly is an tenth generation AI computer, owned by the Jupiter Mining Corporation and installed on Red Dwarf as a backup system to avoid human errors occuring. Whilst all goes to plan in that in the event of a lethal radiation leak, Holly manages to save the one remaining crew member, it takes three million years, and in that time the computer passes its sell by date and loses its marbles.
Clinging desperately to an intelligence he knows he once had, Holly revels in quoting his IQ at six thousand, whilst admitting that he might possibly have gone a "bit peculiar".
His role on board is basically to plot the course and return the crew to Earth in the absence of any other flight co-ordinators and senior crew although he also engages in human passtimes such as chess and reading.
Between such trying intellectual pursuits Holly attends to the crew's general needs, particularly those of Rimmer's since he requires the generation of holographic items to help his existence seem less futile.
Duties like these take their toll on an artificial life form with a penchant for computer senility, and around the time Holly sees a male crew member give birth, he performs a head sex change upon himself, generating a female face and personality which were seen from series three onwards.
Come the end of series five, Holly had become a very small role, with much of her expertise covered by Kryten's more than adequate knowledge. She was last seen on board Red Dwarf before it was stolen or lost whilst parked around a planetoid, and in their search for their home ship, Holly is a sadly missed crew member.