The stolen cars are usually muscle cars, import and domestic street cars, donks and cars of luxury or high trade in value. This practice is very common in cities with many "Chop Shops" such as: Oakland, Detroit, St. Louis, Los Angeles and Las Vegas.
The phrase was made known by the movie "Fast and the Furious" (2001) when Dominic (Vin Diesel) finds out Brian (Paul Walker) was incarcerated for "Boosting Cars".
Dom: Boost cars?
Brian: No, never.
Dom: Do time?
Brian: Couple of overnighters. No big deal.
Dom: What about those two years you did in juvie for boosting cars? Tucson, right? I had Jesse run a little background check on you, Mr. Brian Earl Spilner.
When in a race (normally from a roll) The operator of a "boosted" (turbocharged) car does a tricky maneuver involving applying brakes then adding in throttle to add more brake smoothly to eventually cause the engine to load up spooling the turbine creating boost/power while maintaining a constant rpm/speed so that when the driver lets off the brakes the car takes off like a bullet.
The car on the left brake boosted on that race.... didn't you hear the turbo spooling before they went?