A race between road vehicles - usually two vehicles over a quarter mile straight track and from a standing start. The race is essentially a competition to determine which vehicle has the greater acceleration.
My first thoughts on the origin of the term 'drag race' brought to mind images of horses and hounds chasing after a scent left by dragging a smelly carcass or cloth along the ground. Those thoughts were probably due to the recent increase in the number of drag hunts in the UK, since the rather ineffective ban on fox hunting was introduced in 2005. While it is correct that hounds have been raced along scent trails since at least the early 1900s and that this continues, it turns out that the US sport of drag racing has only a very tenuous connection with anything being dragged along.
To trace the origin of the 'drag race' we need to go back to the pre-supercharged days of the 1500s, when a drag was a heavy sledge that was dragged by horses. This form of cart without wheels was known from the 14th century, under the name of dray. In the 1570s, Elizabeth I introduced various legislative acts that were collectively known as the Poor Laws. The 1576 act included this text:
Sleades, carres, or drags, furnished for... repairing... high wayes.
Road flattening work is these days done using heavy wheeled vehicles called scrapers.
Neither the mediaeval sleds nor the modern day scrapers seem to be the stuff of drag racing, so where's the connection?
That connection comes in the 18th century, by which time smaller drags/drays were being used for the hawking of goods, and the poor souls who hauled them around had the ingenious idea of adding wheels. Samuel Johnson defined such a vehicle in A dictionary of the English Language, 1755:
Drag ... Somewhat like a low car: it is used for the carriage of timber, and then is drawn by the handle by two or more men.
Before long, the term 'drag' came to be used for the thoroughfares along which drags were trundled. The poor get in on the act again (they are always with us, after all) in Henry Mayhew’s London Labour and the London Poor, 1851:
Another woman... whose husband has got a month for "griddling in the main drag" (singing in the high street).
The 'roadway' meaning of drag was transferred from England to the USA and, in the 1950s, the teenage pastime of racing cars 'along the main drag' began to be called 'hot rodding' or 'drag racing'. There are also references to dog drag races in publications throughout the 20th century, but the earliest that explicitly mention cars come from from the 1950s. An example of that comes in this heartfelt piece from The Southeast Missourian newspaper in June 1950, titled Teenage Crime:
"There have been entirely to many hot rod exhibitions of fender tagging and drag racing.
Before long the street pastime became a sport, first taking place on disused airstrips and later on purpose-built drag strips, the US National Hot Rod Association being formed in 1951. So, the link to the original meaning of drag is almost lost - drag racing is no longer done with or on drags and nothing is dragged along.
My initial imagery might have had more linguistic validity had I opted for a picture of camp gentlemen in wigs and frocks racing each other. That 'men dressing as women' meaning of the word drag actually does derive from dragging something along - in that case female impersonators dragging long dresses across the stage.