Autocross is a motorsport that consists of individual timed runs through a course laid out (using traffic cones) on a concrete or asphalt surface. The object is to drive through the course as fast as possible without missing any gates or hitting any cones.
While autocross events typically involve lower speeds than other motorsports (60 - 90MPH) the number of driver inputs per second is comparable to Formula One.
Much like drag racing, autocross has a low cost of entry. Most sanctioning bodies only require a car in good mechanical shape, and an approved helmet. There is usually a class for every car manufactured, so that cars of like type compete against each other.
The largest autocross sanctioning body is the SCCA. The SCCA holds the largest amateur autocross event in the world (The National Championship in Topeka, KS every fall) and also sanctions a professional series called ProSolo.
In SCCA-speak, "autocross" is known as Solo 2 - Solo 1 being high-speed timed events like hillclimbs.