Briefly: current carrying capacity without undue voltage drop.
Every wire has some resistance even a relatively short 12 gauge wire used in a computer PS. So given ohms law V=IR, there will be some voltage drop across that wire that increases with increasing current. Motherboards in particular can be very power hungry and are not very tolerant of voltage variation.
The solution is to reduce the resistance in the path from the PS to the MB or other peripheral. The simple way is the have multiple wires. All those wires connect to the same bus within the PS.