If a circuit operates on 12 volts, you must supply 12 volts to it. If you supply less than that (say, 9 volts), the electronic circuits that require a certain voltage to operate will not function properly, if at all. And, if you supply more than that (say, 15 volts), either the components will not function properly or some will burn out.

The current (mA) rating is a little different. A circuit will only take as much current as it needs, unless the voltage is too high (which is why a circuit will burn out with a higher voltage than it needs). But, if the voltage is correct and a circuit only draws 200 mA (200 milliamps, or 200/1000 of an amp, or 0.2 amps) and you hook it up to that 500 mA adapter, the device will still only draw 200 mA. However, if you have a device that takes 500 mA and you only have a 200 mA adapter, the adapter will try to put out too much current (more than it's rated for) and it will burn out instead.