The story involves the denizens of the planet Mars, including Momar ("Mom Martian") and Kimar ("King Martian") who are worried that their children Girmar ("Girl Martian") and Bomar ("Boy Martian") are watching too much television. Following the advice of a Martian sage or wise elder (or something), the Martians kidnap Santa Claus from Earth and bring him to Mars to make toys for the children of their planet. One warmongering Martian rebels and tries to destroy Santa Claus, as he believes that Santa is corrupting the children of Mars and turning them away from the original glory that Mars used to have.
One scene in the movie uses stock footage of military planes refueling in flight. This is the same footage used during the opening sequence of Dr. Strangelove.
The movie also features a song called "Hooray for Santy Claus" (composed by Milton DeLugg), which the filmmakers must have hoped would become an annual holiday hit. It didn't.
The movie is also the title (and the subject) of one of the most popular episodes of Mystery Science Theater 3000. In addition to original host Joel Robinson and his robot friends giving the movie a much-deserved vivisection with their wisecracks, the TV episode also includes the MST3k comedy segments "The Wish-Squisher" and "A Patrick Swayze Christmas."
For whatever reason, the movie was remade in 2002.