The song follows the story of Peter Pumpkinhead, a man who comes to an unspecified town, "spreading wisdom and cash around." He is extremely popular with the people of the town, but extremely unpopular with government figures. In the end, Peter Pumpkinhead is killed by those he made enemies of, "nailed to a chunk of wood" (probably a reference to being crucified, like Jesus, possibly even comparing the two men).
Many believe "Peter Pumpkinhead" is a pseudonym for and refers to one of various historic figures such as John F. Kennedy, Jesus Christ, or John Lennon. However, the writer of the song, Andy Partridge, stated that he was not referring to any one being, but to such characters and their lives as a whole, namely that their mission to do good resulted in their death brought about by "government" figures.
The name Peter Pumpkinhead in fact came about by Partridge having carved out a Halloween pumpkin and, following the October festival, sticking it on one of the fence posts in his garden. Partridge walked past the pumpkin each day on the way to his composing shed and, feeling sorry for the increasingly decaying fruit head, decided to write a song about him.
There are two different versions of the XTC music video, both of which feature a scenario very similar to the assassination of President John F. Kennedy, although one is heavily edited for US TV broadcast and removes much of the more controversial material. The Kennedy reference is also made explicit by the image of a pig with a map of Cuba superimposed on it - a clear reference to the Bay of Pigs Invasion in 1961. They also briefly feature an actress dressed like Marilyn Monroe during the 3rd verse. In addition, the uncensored video makes brief reference to Jesus Christ by flashing the words "three nails" and showing a crown of thorns. The lyrics "Peter Pumpkinhead was too good; Had him nailed to a chunk of wood" reinforce this crucifixion reference. It also cross references all three stories by strongly implying that the death of all three were caused by some sort of government conspiracy. It is of note that during the last verse of the uncensored video, there are shots of evidence bags marked with the tags "X" (possibly a reference to Malcolm X), "R" (possibly a reference to Robert F. Kennedy) and (together) "J" and "F".
It features Jeff Daniels reprising his role of "Harry Dunne" from Dumb and Dumber. In the video, Harry falls and gets a Jack-o'-lantern stuck on his head. In his struggle to get it off, he foils a bank robbery and becomes a media sensation. However, he is unfairly found guilty of the bank robbery and narrowly avoids being hanged (he is saved by the pumpkin, which is placed on his head before he's put in the noose). It ends with a spoof of the religious imagery in the original video, as Harry's followers (oblivious to him having survived) venerate him as a martyr and establish the "Church of the Latter-Day Pumpkinheads" where they don Jack-o'-lantern masks, ape Harry's struggle to remove the pumpkin stuck to his head, and take communion of pumpkin seeds and wine sipped from a pumpkin stem.