The Coneheads are a fictional family of extraterrestrials with bald conical heads, created for a series of recurring sketches on Saturday Night Live (SNL).
Beldar states his occupation as "timekeeper of Remulak"; this means he is a spy tasked with alerting his home planet to the optimum time for an invasion of Earth, which he fails to do.
Connie is assimilating with Earthlings through association with her peers at school, and some family stress is caused by her desire to live as a typical Earth teenager.
The Coneheads have much larger appetites than Earthlings, eating large amounts of food during meals (which they identify by another one of their catchphrases, "consuming mass quantities").
[1][2] Dan Aykroyd also mentioned in an interview that he drew inspiration from the film This Island Earth where the very tall foreheads of the aliens go largely unnoticed by humans.
When he hosted SNL, Zappa also appeared in a Coneheads sketch as a man dating Connie, where he makes note that he prefers French women.
The feature film was licensed to Playmates Toys and a line of action figures was created, designed by the development team from Pangea Corporation.
When the microwave breaks, the Coneheads (Aykroyd, Curtin and Newman) invoke their State Farm representative by singing the company's jingle.