A coin meter is a common component in many different types of coin operated equipment, such as arcade games, slot machines, electromechanical games, and older soda machines.
The coin meter is basically like an odometer. It has a mechanical numerical display that increments by one each time a coin is inserted. Some machines will also increment the coin meter if you add a credit using the service switch, while others will not.
The main use of the coin meter is to let the game owner know how many coins are supposed to be in the coin box. It also has a secondary function of giving you a rough idea of how many times a machine has been used. But you can't always go by the coin meter, as they are easily replaced, or unwired. Plus an older machine might have a twenty year old meter with 200,000+ showing, yet all the machines internals could possibly be a lot newer than that.
Most coin meters are powered by a simple electromagnet. 12 Volt coin meters are currently the most common, but some older machines use 24 Volt ones, and a few use 6 Volt ones. The meter isn't actually set off by the act of dropping the coin, but it is actually set off by a pulse of power it receives from the main circuit board of the machine.
Almost all arcade games support these meters, including all games compatible with the JAMMA or Konami Standards.
New coin meters usually run less than $10. The meter itself will have two wires coming out of it. To install one, simply check and see if your machine's wiring harness has a wire for "Coin meter 1", if so, then attach that wire to one of the coin meter's wire, and the attach the other coin meter wire to ground.
You can usually reset the meter by taking it apart and rolling it back by hand, but a few meters will have a reset button on them.