In an ATX power supply, how is the -12V supply made?
It is indeed a -12V rail. Frequently used in audio circuits and for RS-232 driver circuits. There used to also be a -5V rail used by ISA cards.

All a negative voltage is is a voltage rail which is at a lower potential than the 0V reference point we call ground. Remember that voltages are all relative - hence the name potential difference. For example if you have a 9V battery you could call the positive terminal ground and the negative terminal would now be -9V. It's entirely down to where you measure from.

There are loads of ways of making negative voltage rails including switched capacitor inverters, DC-DC converters amongst other ways. Mains AC alternates positive and negative, and consequently with two diodes and a couple of capacitors you can make a negative and positive voltage rail. Centre tapped or multiple secondary transformers can/are also be used for this purpose.