Ampacity
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Ampacity is the rated electrical current-carrying capacity for a conductor in a given situation, as addressed by the National Electric Code. It takes into account the gauge of the wire along with the type of insulation, proximity of other current carrying wires, ambient temperature, and other factors.
Wires are heated by the Joule heating caused by the electric current flowing through them. Copper or aluminum wires could conduct a large amount of current before melting but long before the conductors melt, their insulation would be damaged by the heat. So the ampacity of a given wire is set by the maximum temperature that the insulation can withstand forever. For common plastic insulations, this may be 60, 90, or 105 degrees Celsius. Bundling multiple wires together increases the amount of heating while decreasing the convection cooling of the insulation; this has the effect of reducing the ampacity for wires in bundles. For example, the National Electric Code specifies that a single 8 AWG copper wire with common insulating material has an ampacity of 50A; this same wire's ampacity drops to 40A when bundled together in non-metallic sheathing with other conductors.
