Virtually every car ever built in some form of series production has been identified by some alpha-numeric sequence. This sequence of numbers and letters has been used by different companies to indicate different things. In the 1920's and 1930's, when coachbuilt cars were popular, vehicles often had three different identification plates: a body number, an engine number, and a chassis number. Duesenberg's, for example, had a three digit engine number (such as J-446), which would identify when the engine was made in the sequence of all Model J engines (starting with J-101 and ending with J-588). The chassis was marked with a four digit number, which, like the engine, identified when the chassis was made in the total sequence of all Model J chassis (starting with 2125 and ending with 2614). You're probably thinking that this meant that the engine and chassis sequences would match, right? Well they didn't because engines and cars were built on separate assembly lines, but there are records of which engine went with which chassis and not all engines or chassis stayed together.
As such, in its most basic form, 'numbers matching' simply means the car (or chassis) has the same engine block that it left the factory with initially. Pictured are an example of a numbers matching Ferrari, in this case, a 1967 Ferrari P412 Mark 3-4. This very important and rare sports-racing car features two separate stampings, one for the engine and one for the chassis. Unlike Duesenberg, the chassis and engine stampings were meant to go together as a pair for this series of vehicles. As you can plainly see, both numbers are identical, indicating that the engine block is the same one that the car left the factory with.
But that is the most basic definition, the meaning of 'numbers matching' for a muscle car is much more complex. As they say on television, "tune in next time for the conclusion of this exciting mystery!"
Pictures, clockwise from lower left, the Chassis Plate for a 1925 Diana Light Eight Sedan the 1967 Ferrari P412 Mk 3-4 Chassis Plate, Ferrari Engine Plate (notice that they are the same number), the whole Ferrari, a 1929 Duesenberg Model J Convertible Sedan (Chassis No. 2284, Engine No. J262, Murphy Body No. 923), Body plate for the Diana, the entire Diana, the Diana's engine plate.