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It's basically a race against the clock in a parking lot around pylons!
Add: Usually low speed (max 70 mph on the longest straight). One by one with your best time counted in the best of 3 or more runs. If you've never seen one perhaps equate it to downhill skiing; more specifically giant slaloms.
Lots of fun and much harder then it seems. Check out the auto cross section on the forum or any number of auto cross web sites. They have some great videos that can give you an idea of what it's like. Give it a try, it's great fun!
Around here, autocross events are usually held on unused airport runways with courses layed out with cones. Various clubs (Porsche, BMW and Corvette) usually sponsor the event. NCCC and SCCA events accumulate points for drivers and clubs.
Sanctioned events usually mean certain safety requirements have to be met which normally means you have to wear a helmet and seat belt. Modified cars may be required to have equipment up to roll cages, fire extinguishers and cut off switches. Also, sanctioned events are considered driver education (not racing) and do not affect your insurance.
Many also offer driver's education classes on becoming a better driver and getting more out of your car.
If you think you know how to handle your Corvette and get the most out of it - sign up for an event and find out how much there is to learn.
It won't hurt your car but does take a bit off your tires.