Sometimes I can get a bit technical. Racing is chock full of terms and slang words that mean nothing to sane people. If I go on a technical rant, you can use this guide to help make sense of it. This is kind of an ongoing project and I'm always adding to it as I think of things.

Apex: the point at which the car is the closest to the inside of a corner. The apex is critical to optimizing the geometry of a turn in order to gain the most speed. Also known as clipping point.
ATGATT: All The Gear, All The Time. Mostly a motorcycle term, but also describes racing drivers who refuse to wear street clothes, preferring to stay nice and safe in their helmet and fireproof overalls.
Camber: The vertical alignment of a wheel. When a car is cornering, the tire will tend to fold under the rim of the wheel. If the rim is perfectly vertical, less of the tire will be in contact with the road and the car will lose grip. Positive and negative camber adjusts for this. Negative camber means the top of the wheel is angled in towards the body. Positive camber means the top of the wheel is angled outwards from the body. Generally, oval racing cars use positive camber on the inside wheels, while road racing cars will use negative camber on all four wheels. Expressed in degrees of alignment.
Caster: the incline of the front suspension. Increasing the incline of the front suspension will adjust turning characteristics, as well as steering feel. No caster setting (no incline) will mean the tires turn normally by twisting horizontally. Adding forward or positive caster will cause the wheels to tilt more vertically, like a motorcycle leaning in a turn. Adding caster will also increase the weight of the steering wheel in turns, and cause it to snap back to center more quickly. Expressed in degrees of alignment.
Coil-over: a coil-over is a type of suspension setup where the spring and the damper of the suspension are put together in one small, light, easily changeable package. As the name implies, the damper is inserted inside the spring. The spring is clamped between perches attached to the housing, with mounting joints at either end for easy install. Coil-over kits usually feature adjustable spring perch and damper settings, and make it easy to change springs for more or less stiffness. See also: spring perch.
Counter-steer: the act of giving the wheel a flick or a spin into the direction of a slide or drift, in order to stop the car from sliding. Also known as opposite lock.
Damper: a damper is a device used for controlling the "bouncyness" of the main spring in the suspension of a car. Without a damper, the chassis would be free to ride the rebound of the main spring, and would bounce up and down uncontrollably after going over a bump. The damper is filled with viscous fluid, and as the damper housing is moved up and down, fluid is forced from one chamber to another via a small hole. The size of the hole determines the rate at which the fluid flows, and thus, the rate at which the damper compresses or extends. This interaction generates heat, dissipating the energy contained in the spring and dampening the undulation of the spring. Most competition dampers are adjustable both in compression (called bump) and extension (called rebound, though, the damper itself does not actually "rebound" - it simply extends as the suspension spring decompresses). Many dampers also have further adjustments to both high-speed and low-speed compression, which allows engineers to adjust the damper to control body roll (low-speed compression) as well as deal with bumps in the road (high-speed compression). Also known as a shock absorber.
HANS device: stands for Head And Neck Support device. A device that sits on the shoulders of the driver, attached to the sides of the helmet and held down by the shoulder belts. Designed to reduce the risk of basilar skull fractures and other neck-related injuries in the event of a crash.
Heel-toe: heel-toe is a technique used for downshifting. Heel-toe is the act by which a driver, while braking with his right foot, uses the same foot for tapping the throttle, either by using the ball of his foot for the brake and the heel for the throttle, or the heel for the brake and the toes for the throttle, or by covering both pedals with his foot and simply rocking it to the right to tap the throttle while pressing the brake. The left foot operates the clutch. The purpose for this technique is outlined under rev matching.
Oversteer: a vehicle handling symptom by which the car has a tendency to slide the rear tires in a turn. Extreme oversteer often results in a spin. The driver can also induce oversteer. A very common cause for oversteer is by simply being too harsh with steering or pedal inputs. Also known as loose.
Push-rod: push-rod type suspension is a method used to transmit the forces of the suspension movement via a strong rod to a remote location, housing the spring and damper (usually using the coil-over setup). This allows the heavy spring and damper to be centrally located on the car, rather than near the wheels, which improves the center of gravity as well as improving aerodynamics in open-wheel formula cars. An alternate setup, known as pull-rod, can also be used in a slightly different fashion.
Rake: when used in the context of vehicle setup, rake usually refers to the relative height of the front and rear of the car. More rake means the rear of the car is higher than the front. This changes the roll dynamics of the car and can be used to cure handling issues.
Rev matching: when a driver changes gear, the RPM of the engine will change. After an upshift, the RPM of the engine will drop. After a downshift, the RPM of the engine will rise. For this reason, during a downshift, in order to be mechanically sympathetic, the driver must use the throttle to manually raise the engine's RPM before completing the gear change. If done improperly, or not done at all, the transmission and various other parts can take a pretty good beating. Also known as blipping.
Slip angle: Since a tire is rubber, it flexes. When the tire is going round a corner, it flexes and twists according to how hard it is cornering. Slip angle is expressed in terms of degrees of rotation, or degrees of slip, ie, 6 degrees of slip angle = tire is turned 6 degrees relative to the direction of actual travel.
Slip ratio: Like slip angle, since a tire is rubber, it flexes. When a car accelerates or brakes, the difference in wheel hub speed and road speed is taken up by the tire, which stretches between the two. Slip ratio is expressed as a percentage of difference in speed, ie, 23% slip ratio = wheel hub spinning 23% slower or faster than the road speed. Watch a slow-motion dragster launch to see this graphically.
Spring perch: the spring perch is where the main spring in the suspension connects with the chassis of the car. In coil-over type suspension, these perches are usually adjustable in some way. This is a quick and easy way to change the ride height of the car. See also, coil-over.
Toe: toe is a term used to describe the horizontal alignment of the wheel. Positive toe has the tires facing slightly inward to the body. Negative toe has the the tires facing slightly outward from the body. More toe generally means worse straight line speed and increased tire wear and heat, since the tire scrubs as it travels down the track askew, but handling issues can be solved with toe settings. Usually expressed in 32nds of an inch from straight ahead.
Track-out: the point at which the car exits a corner, and meets the outside edge of the road or the rumble strip.
Turn-in: the point at which a driver begins transitioning the car to full cornering mode. This is not always when the steering wheel is first turned, rather, it is the point when a driver "sets" the car on the line through the corner that he desires.
Understeer: vehicle handling symptom by which the car has a tendency to slide the front tires in a turn. Extreme understeer can result in an inability to turn the car. Also known as tight, or push.
WOT: Wide Open Throttle.