Recently a couple of people have asked about the 6v rectifier which is a small silver box, often found under the seat, that converts or 'rectifies' AC from the magneto to DC for battery charging etc. On the KH125's it also does the job of a regulator, ensuring that the battery is not over charged by 'regulating' power flow. Therefore the device is often referred to as rectifier/regulator.
The KH125 can be started and run without a rectifier/regulator being connected but the battery won't charge. Also, the bike can be started without a battery being connected but prolonged use like this can fry the rectifier/regulator as the power has nowhere to go. There is also a small diode located after the fuse (within some heat-shrink) that is supposed to stop the battery from discharging - though a non charging battery is more likely to be caused by:
A bad battery
Broken fuse
A bad earth from battery to frame
A brake in the magneto, regulator/rectifier, battery, wiring circuit
A fried regulator/rectifier
Wiring plug working its way off the regulator/rectifier through vibration
Regulator/rectifiers are one of the parts that go missing on old bikes, usually with the three pin plug that connects to it as well. I've included a picture below showing which wires go where. (View from rear toward front).