According to Björk, the song is about a little girl who is out biking and sees "a motor crash, and no police has arrived yet, and there is a car with parents in the front and children in the back and they're all wounded. And she wants to help them - so it's a really nice song."
The girl in the song then sneaks the mother in the motorcrash into her house and nurses the woman's wounds there. When the mother is healed, she and the girl disguise themselves and take a taxi to the woman's home. When the woman's husband opens the door, she and the girl pull off their disguises.
"But the husband gets very angry," Björk explained, "and says, 'Where have you been all this time?' And then the song is over."
Lyrics about motorcrashes (or as Americans call them, car accidents), are not typically paired with jaunty music as heard here, but The Sugarcubes were not a typical band. The subject matter turned off some major record labels, including Polydor, which pulled plans to sign Sugarcubes because of the perceived offensiveness of "Motorcrash." Björk explained that labels' reactions were absurd because the song wasn't about anything mildly offensive.
The Icelandic director Óskar Jónasson was behind the lens for the video, which starred the band members as the characters described in the song. Their keyboard player, Magga Örnólfsdóttir, is the girl on the bike.