In these films Father Christmas is depicted as a horrific monster, a near-feral madman who while capable of being "tamed" for a short while is incredibly dangerous and as far removed from the lovable elf of folklore as imaginable.
Father Christmas is depicted as supernaturally strong, aggressive and driven almost purely by a predatory instinct that sees him mercilessly slay any who get in his way.
The films revolve around the efforts of an elite-group of scientist / bounty-hunter stereotypes in capturing and subduing this fearsome beast while the narrator speaks much like a documentary host as he describes in deadpan-style humor the atrocities Father Christmas can commit (as well as ways to survive his wrath).
Rare Exports Inc.
Father Christmas is first seen in Rare Exports Inc where he is depicted as naked wild man incapable of speech yet being stronger than a bear and capable of amazing speed - even when shoot multiple times with tranquilizer darts the monster keeps on running (though it is worth noting in this movie he runs away from the hunters rather than towards them).
After being captured Father Christmas is showered and put through a rigorous test in order to tame his wild nature, using a fake child which the elite-hunters put on his knee and try to encourage him to talk to (much as a mall Santa would do).
However the feral Father Christmas instead continually tries to devour the fake child, earning a few disciplinary slaps from the elite-hunters (much like training a wild animal) - eventually Father Christmas is tamed and packaged away.. though the fact he is still kept in a cage means it is debatable how tame he truly is.. (this is further eluded to in the next movie).
Rare Exports: The Official Safety Instructions
In Rare Exports: The Official Safety Instructions the now "tamed" Father Christmas is shown to be far from benevolent after all as the narrator (in typical deadpan-style) details the rules one must abide to in order to prevent Father Christmas reverting to his natural state as a monstrous killer.
Loud noises cause discomfort to Father Christmas and will provoke him into attacking those responsible, smoking will cause Father Christmas to home in on the offender and according to the narrator he has been known to tear the lungs out of those who smoke in his presence: though playing dead may save one's life.
Disrepectful behaviour (such as spitting) can also cause Father Christmas to lunge at the offender and maul them, however the most dangerous thing one can do in the presence of Father Christmas is drink and swear - this was shown in the movie with a comedic scene in which a drunken man smashes a bottle and swears at Father Christmas, who is locked inside a cage: the sheer rage Father Christmas feels is sufficient to shatter the cage (complete with a Hulk-style roar) and Father Christmas leaps at incredible speed towards his victim.
The rest of the movie shows a disturbing scene involving a rogue Father Christmas, who has massacred a large group of people - a young boy is approached by the beast and manages to appease him via feeding him a gingerbread cookie: however Father Christmas (still covered in blood) continues to eye the boy like a hungry predator.
Eventually the boy's father and an elite-hunter arrive on the scene, the father covers the boy's eyes while the other hunter shoots the rogue Father Christmas dead: as once the rules are broken it is impossible to stop Father Christmas (this is a dark parody on the fact man-eaters, once they taste human flesh, can not be trusted and often have to be killed).