Multiple +12V Rails
As power supply capacity increased, the ATX power supply standard was amended to include:
3.2.4. Power Limit / Hazardous Energy Levels
Under normal or overload conditions, no output shall continuously provide more than 240 VA under any conditions of load including output short circuit, per the requirement of UL 1950/ CSA 950/ EN 60950/ IEC 950.
—ATX12V Power Supply Design Guide, version 2.2
This is a safety limit on the amount of power that may pass, in case of a fault, through any one wire. That much power can significantly overheat a wire, and more would be likely to melt the insulation and possibly start a fire.
Because implementing one current limit per wire is prohibitively expensive, and the limit is far larger than the reasonable current draw through a single wire, manufacturers typically group several wires together and apply the current limit to the wire as a group. Obviously, if the group is limited to 240 VA, so is each wire in it. Typically, a power supply will guarantee at least 17 A at 12 V by having a current limit of 18.5 A, plus or minus 8%. Thus, it is guaranteed to supply at least 17 A, and guaranteed to cut off before 20 A.
These are the so-called "multiple power supply rails". They are not fully independent; they are all connected to a single high-current 12V source inside the power supply, but have separate current limit circuitry. The current limit groups are documented so the user can avoid placing too many high-current loads in the same group.
This works in the same way, and for the same reason, as the many small circuit breakers in a circuit breaker panel as well as the main supply breaker. And just like typical domestic wiring, multiple outlets are connected to each circuit breaker for reasons of cost.
Originally, a power supply featuring "multiple +12V rails" implied one able to deliver more than 20 A of +12V power, and was seen as a good thing. However, people found the need to balance loads across many +12V rails inconvenient. This problem was exacerbated by the fact that the assignment of connectors to rails is done at manufacturing time, and it is not always possible to move a given load to a different rail.
Rather than add more current limit circuits, many manufacturers are ignoring the requirement and providing "single-rail" power supplies that omit the current limit circuitry. Although capable of starting a fire under the appropriate circumstances, there have not been a noticeable increase in accidental fires, and as of 2008, product safety testers like Underwriters Laboratories continue to approve the supplies.
For a time, power supplies were marked and sold as having multiple +12V rails, although no current limit circuitry was included. As of 2008, having only an overall +12V current limit is seen as a desirable feature, and "single-rail" power supplies are advertised and sold as such, although it is still common to find power supplies for sale that falsely claim to have multiple +12V rails.