In simplistic terms, it means "the chassis, engine, and transmission are all the ones that came together from the factory." In practice the actual "proof" varies a bit between manufacturers and even over time with the same manufacturer.
In specific terms, say for my 1969 Coronet R/T, the full vehicle VIN is stamped on the placard that is riveted to the dash. The VIN is also stamped in 2 other locations into the metal of the chassis itself- the radiator core support, and under the weatherstripping of the trunk lip. Having all of those together and the same (without tampered rivets on the dash placard) makes the full chassis "numbers matching." Having replaced suspension components, brakes, etc. doesn't matter because those aren't uniquely identified to the car in the first place.
The engine has a PARTIAL copy of the VIN stamped on the block just above the oil pan rail, and so does the transmission. Those partial VINs match the 3 VINs on the chassis, so the complete vehicle is "numbers matching."
It is also preferred if the fendertag under the hood matches the VIN, all the options it shows match the actual vehicle, and best of all if a matching paper "build sheet" was found in the car (my build sheet was long gone, for that car, although I have it for my '66.) The "build sheet" was used by workers as the car passed down the line and they installed various equipment that it called out. It wasn't ever required to stay with the car, but it was common practice to stuff it between the springs and foam of the rear seat at the end of the line (at least for Chrysler products).
It is different for years when there were different numbers of VIN stampings and different stamping locations. Other manufacturers differ as well.
Usually there's some leeway granted in special cases, or at least there used to be in the collector car community. For example, an engine that was a factory dealer replacement would have a special tag identifying it as a warranty engine, but no VIN matching the car. All in all, the whole "numbers matching" thing seems to matter a lot less than it did 20 years ago.
