The song describes a future in which many classes of vehicles have been prohibited by "the Motor Law". The narrator's uncle has kept one of these illegal vehicles (the titular red barchetta sportscar) in pristine condition for some "fifty-odd years" and keeps it hidden at his secret country home (previously a farm before the enactment of the aforementioned Motor Law). Every Sunday, the narrator sneaks out to this location and goes for a drive in the countryside. During one such drive, he encounters a "gleaming alloy air car" that begins to chase him along the roads. A second such vehicle soon joins the pursuit, which continues until the narrator drives across a one-lane bridge that is too narrow for the air cars. The song ends with the narrator returning safely to his uncle's farm.
The song was inspired by the futuristic short story "A Nice Morning Drive", by Richard Foster and published in the November 1973 issue of Road and Track magazine. The story describes a similar future in which increasingly stringent safety regulations have forced cars to evolve into massive Modern Safety Vehicles (MSVs), capable of withstanding a 50-mile-per-hour impact without injury to the driver. Consequently, drivers of MSVs have become less safety-conscious and more aggressive, and "bouncing" (intentionally ramming) the older, smaller cars is a common sport among some.
Rush lyricist Neil Peart made several attempts to contact Foster while working on the album, but Road and Track did not have an up-to-date address, and Rush were forced to settle for a brief "Inspired by" note in the lyric sheet mentioning the story. In July 2007, Foster and Peart finally made contact with one another; Foster later posted an online account of their journey by motorcycle through the backwoods of West Virginia between stops on Rush's Snakes and Arrows tour.
Barchetta, literally "small boat" in Italian, is the diminutive form of barca ("boat" or "craft"). In the automotive industry, the term is used for a 2-seat car without any kind of roof. It is normally pronounced Italian pronunciation: [barˈketta].