An automotive term used to describe the originality of a car. Different major components of a car carry serial numbers, and when a vehicle is manufactured, the numbers are recorded. Therefore, one can find out whether the original components are still present. If they are, the vehicle is said to have matching numbers: in classified ads, one might find the phrase 'numbers match'.
Generally, the numbered items are the frame or bodyshell, the engine, and the transmission.
A vehicle old or rare enough to be considered collectable will be valued much more highly if the major components are original. Part of this is simply to do with originality - for many collectors, the ideal car would be a zero-mileage, untouched vehicle sealed in a box, and the further a car is from this ideal state, the less it is worth.
The other reason that a car without matching numbers is less valuable is simply because, in order for the numbers not to be matching, there must have been a motivation. It costs a lot of money to swap an engine or other major component.
One possibility is that something happened that required things, normally the engine or transmission, to be replaced - and that normally means the car was damaged or poorly looked after. It's an indicator that other, unreplaced parts of the car may also be in poor repair. On a performance car, a muscle car for example, it may reveal a car that has been badly abused or raced (legally, or more likely otherwise).
Alternatively, it was owned by someone who liked to modify and customise their vehicle. Most people who do this do a very poor job, and it's a rare modified car that's worth more than the original.
As pointed out by a user, checking to see if the numbers match is also a way of ensuring the car you're buying isn't a stolen car reincarnated by giving it the VIN of a wrecked car. If the engine, transmission and chassis numbers aren't right, which can be checked these days with a variety of services, and there's no matching service record, be very careful! | 
