hydraulic valve lifter: A lifter that uses hydraulic oil pressure to maintain no clearance between metal parts so that valve noise is reduced. Also it reduces wear on the valves and eliminates periodic valve adjustments.

quad-cam engine: An engine with four camshafts

barrel: The air horn in the carburetor. In particular, it is that part where the throttle valve is located. If a carburetor has four openings with a throttle valve in each, it is called a "four-barrel carburetor."

fuel injector: The device that works like a hypodermic needle to inject the proper amount of fuel into the combustion chamber in response to signals from an electronic sensing device on cars with fuel injection systems. It receives fuel at low pressure and shoots it into the engine cylinders at predetermined intervals under higher pressure.

deceleration fuel cut-off: A device which stops the flow of fuel to the carburetor or injectors when the vehicle rapidly decelerates in the event of a crash thus preventing the possibility of a fire or explosion.

chrome-plated: In order to prevent iron from rusting, parts are coated with a layer of chromium by process of electroplating (or electrodeposition).

connecting rod: The connecting link or arm between the piston and the crankshaft. It converts the up-and-down (reciprocating) motion of the piston into the circular (rotary) motion of the spinning crankshaft. Often called "con rod."

four on the floor: A four-speed manual transmission with floor mounted shift.

the quarter mile: Drag racing is a form of auto racing in which any two vehicles (most often two cars or motorcycles) attempt to complete a fairly short, straight and level course in the shortest amount of time, starting from a dead stop. The most common distance is one quarter mile (402 m / 1320 ft.).

heat lap trial -- a one-lap race or "heat" to determine starting positions in the actual race

frenched tail lights: The customizing process of creating smooth curve shaping around the headlights, tail lights, license plate frames, etc. so that the actual lights, etc. recede a little towards the interior of the panel opening and the chrome bezel or other surround looks as though it is part of the body panel.

fins: Wings and airfoils used to improve a vehicle's aerodynamics, stability, or possibly aesthetics.

palomino dashboard: palomino leather interiors were the top of 50s and 60s automotive fashion, sometimes including palomino leather dashboards

dual muffler twins: An exhaust system with two tailpipes; either a complete exhaust system, as on performance cars and cars with V-engines, or simply two tailpipes emanating from the rear muffler.
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And here is a description with photos of the kind of work Kenickie intends to do on his car -- http://www.nationalhotrod.com/html/features_2.html